Thanks to fellow tourers who have been very generous with information, offers and tips.

Collation of the posts I have received:

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-- Use Old Tumbarumba Road from Gilmore to Batlow - steeper but much less traffic than the main road.
-- Get ahold of the Hume and Hovell journals and have a read before riding from Tumba to Jingellic. The road follows much of their route, and from Munderoo area to the drop off the plateau to Jingellic, you'll be looking at what they looked at. Good history fun!
-- Pub meals at Jingellic Pub are nothing special but good value for $$. You can camp below the pub for free and showers are available for a small fee. However, this spot can get really packed out with the caravan crowd. For a similar cost of a pub feed and shower, you can camp at the caravan park in Walwa. It is rarely crowded, facilities are good and the owners are nice (they have let me leave my car there while I did multi-day rides from there). I think you could also get away with camping nearby at the Jingellic showground without being bothered - toilets and water there, too. There is also a reserve on the VIC side of the river near Jingellic - no toilets but quieter. You can get a toilet stop at the Kurrajongs downriver (camping here too).
-- If you are contemplating the gravel road on the NSW side from Jingellic to Wymah... ask at the pub about the road condition. I've ridden it a few times and the condition can be downright horrible when it hasn't been graded recently. I have found it to not have that much less traffic than the paved VIC side and is MUCH slower riding. There are not a lot of camping options over on the NSW side (just fishing access sites - which I don't think are technically legal for camping - and a couple TSRs), either. If you aren't fussed about gravel vs paved, definitely ride the paved VIC side. There really isn't that much more traffic.
Page: Kurrajong Campsite to Woomargama National Park via Guys Forest, Walwa and Talmalmo, in journal "Neither Here nor There" by Emily Sharp (Completed Dec 2015) in Bicycle Life
-- The pub at Granya has reopened in the past few years. Decent meals. They have very basic motel-type accommodation and you can camp there for free. Water and drinks available if you don't need food or accommodation. You can also head up the road to Mt Granya State Park to camp. Toilet, but no water unless creek is running. The camping area here isn't all that attractive (it's the back paddocks of an old dairy and feels like you are camping in someone's backyard). The secret here is to take the MVO track up to the old Scout Hut and camp there. It's a nice setting, and you get away from the caravans down in the campground and away from the adjacent private landowners who like to shoot rabbits in the evening.
Page: Clarkes Lagoon Reserve - Walwa - Granya, in journal "4,000 for 40" by Emily Sharp (Completed Jan 2017) in Bicycle Life
-- If you are contemplating coming into Albury from the north via Wymah, be aware the back road from the old highway alignment/frontage road to Ettamogah is not passable when Lake Hume is over about 80 percent. The freeway is your only alternative. Southbound freeway is okay though, as the shoulder is acceptable and concrete instead of chipseal as it is the newer side when they duplicated the road.
-- Riverina Highway between Albury and Howlong is not very fun - quite busy, sections with no shoulder, no views of the river. I see cyclists on this on occasion, but I don't ride it. I will give you a scenic but circuitous route through the Bungowannah hills, that I've ridden many times, on the map below. At Howlong (camping just over the river by the Lions Park), cross over the river and use Goorramada and Up River Roads to Corowa instead of the Riverina Highway. It doesn't have a shoulder but has a little bit less traffic, goes closer to the river and has fewer trucks (particularly at harvest time). The Riverina Highway through here has lots of sections with no shoulder and most of the trucks.
-- There is camping at Corowa near the Federation Bridge and out at the Commons by the golf club. No toilets or anything at either though. I'm living at Corowa (and saving $250/month in commute costs), and you and your friend are welcome to stay at my unit. I have very limited furniture and no beds, but plenty of floor space and spare rooms if you want to 'camp' in my unit. Even if you prefer to camp near Corowa and come up for a shower and/or feed, that'd be fine. If you are just passing through during the day and want a shower, you can come down to the Council offices and I can give you the key to my unit (I live about 5 min from the offices/info centre).
-- Corowa to Mulwala. Spring Drive has some traffic, but it's usually not too bad outside of school holiday times when there are LOTS of vehicles with boat trailers. There are several reserves along the river through here where you can camp (I never have, so don't have recommendations). Federation Council just got funding to build a bike path between these two towns (yay!), but I don't know the details yet, since I was away when they got the tick. I don't know timeframes either.
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When wild camping try to top up your water supplies from the towns you pass. Below about Tocumwal I found the river water too turbid to even filter, but your mileage may vary depending on seasonal flows. The wild camping is great but best to avoid the river between Christmas and New Year when both the river and any accessible beachfront are choked by the revving masses - honestly if it floats or has wheels and a motor they'll be there revving the hell out of it until they collapse in a drunken heap late at night.
If you're really keen on starting at the source of the Murray you can access that at Cowombat flat via the Cascade and Cowombat Trails in the Kosciuszko National Park. Although you then have a big detour into Victoria to rejoin the river at either Tom Groggin (via 4wd tracks) or nearer Towong (via Corryong) or at Albury itself.
Rode from Mildura to Adelaide via the Murray as best I could and loved it. But need to complete the section from Albury to Mildura some time. Like the history of the area and could easily retire up that way. Hope they've made the road wider near the Dunlop tyre going into Renmark, the trucks drove me crazy there. Go to the mouth of the Murray at Goolwa, look at the wharf at Morgan, spend time in the Museum at Mannum and enjoy the lovely views along the way. The Sturt get busy so maybe ride the northern side of the river from Berri to Waikerie. I crossed the river to the North at Cadell and then back over at Morgan.
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Hi Graham, in 2012 followed the Coorong and around the lower lakes to Goolwa, nice road, I found Princess Highway was quiet. I also went from Mannum to Renmark using paved roads that nearly all avoid the Sturt highway. Taking a northern route from Morgan to Barmera, haven't written this trip up by can share more info.
I have also done some sections beside the Murray between Vic/Nsw border, upper Murray between Towong and Hume Dam is my favourite, your close to the river at the start before your high above as the Hume dam begins. I'm hopefully redoing this next week, it's all paved on a quiet road.
Between Corowa and Mulwala is quiet road but your mostly out of site of the river because of trees until Lake Mulwala. The Vic side is the busy Murray Valley highway. I have canoed between Tocumwal and Barmah and the only roads are dirt and it can be flooded. Between Barmah and Echuca is a nice gravel road options that goes past the Goulburn River junction with the Murray River.
Nice dirt road beside the Murray River between Koondrook and Murrabit but only highways past Swan Hill beside the River, there is a dirt road option through Hattah National Park but haven't been so can not confirm but it could connect with paved route to Mildura. Any roads between Wentworth and Renmark is dirt or the Sturt Highway. Never done a whole trip but I would advise avoiding the Murray Valley and Sturt Highways.

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This all sounds damn nice.

And whatever you do, it will be more enjoyable than the Hay Plain in Summer!

Roads from Morgan down near the River have plenty of easy access to the River, if not on the road, on a short side road. They are also relatively quiet roads for cars. Down this way, the River is bounded a lot/most of the time by huge cliffs, quite spectacular. It does mean that the roads are often on the plain on top of the cliffs, but they aren't far from it.

From Morgan I would ride the west side to Blanchetown at the least, in the last few years I think all of that has been bitumenised (I was shocked a couple of months ago seeing Bitumen to Roonka). You could contact Roonka Scout Camp to see if you can stay there a night; showers etc, on the River, cheap.

http://www.roonka.sa.scouts.com.au/about.html

If you are riding back to Adelaide afterwards to get home, I would probably ride back to Murray Bridge, then follow the Old Princes Highway (you can't ride on the new one, the freeway). Its a fair hill ride, but pretty enjoyable. Once you get to Crafers, take the Old Highway which is now an awesome downhill (sealed!) bike track past Eagle On the Hill. Overtake Lycra clad roadies with your Thorn ;-)

*I definitely wouldn't take your own River water in SA, certainly not South of Waikerie. Salt. Not good for you, even if you filter out the rest of the muck we inherit from interstate. Try and get town water or rainwater for sure. At the least, when we use River water in SA for domestic purposes, SA Water are very careful to try and take it from places where the salt content is lower and more fit for human consumption.