I have not measured the rims with the tyres removed but with calipers across the widest part I get 2.7" This concurs with what Rusty has measured in his post, so that confirms, for me at least, that it IS a WM2 rim.
Which then also concurs with the "T100T
" in the details beside all your posts; also, the qd hub would've been more-likely fitted to a T100T than a T100R. Pre-'71, it's only the US-market T100R and T100C that originally had 4.00-width rear tyres on WM3 rims, T100T (and T100S) had 3.50-width rear tyres on the WM2 rims.
I am aware that tyres have got bigger.
It wasn't in your earlier posts. You asked for help, I'm telling you what I know - irrespective that the numbers moulded on Roadrider sidewalls are the same as printed in '69 Triumph 500 manuals, Roadriders in those sizes are the wrong tyres for your bike, particularly as you've now confirmed the rear rim is narrower than the minimum 2.15/WM3 for a 4.00-width tyre.
I looked at changing to K82s but they don't do anything in 19" sizes so a non-matched pair would be yet another problem. The nearest in tread pattern would be a K81/TT100 front, but there's no guarantee the compounds are similar to the K82.
You are over-thinking.
Any '69 T100 will struggle to exceed 25 bhp at the rear wheel, it isn't the latest mega-bhp plastic rocket. If there'd been anything wrong with K82 on the rear and another model or make of tyre on the front, I wouldn't have advised it. Otoh, I have advised that you reduce the width of the front tyre with the K82.
Avon/Dunlop combinations on more-powerful triples pre-date Roadriders by decades - 'front-only' Avon tyre on the front, TT100 on the rear. My experience of those tread combinations is precisely why I recommended it.
However, if you really must have a similar tread pattern on the front, 3.60x19 TT100 is available in GB, 3.60 is the nearest Imperial low-profile 'equivalent' of 90/90. "compounds" will not be something that affects your bike, trust me.
You posted , "I'm stuck with a Roadrider 90/90 metric tyre as the only fit on a WM2". Roadriders are not primarily intended for low-powered bikes; if you insist on unsuitable tyres and other bizarre arbitrary restrictions, yes, you're "stuck".
A 90/90 metric rear would fit the existing rim but would seriously under gear the bike as it's so much smaller (2") in diameter.
Which is why you should use a more-suitably-sized rear tyre. A 3.50-width tyre is a similar height to a 100
I was already going to change to a 43t rear sprocket and/or a larger gearbox sprocket as I feel the standard gearing is too buzzy.
Depends what you change the rear hub to. 43-tooth pre-dates 46-tooth; non-qd drum takes a bolt-on sprocket so 43-tooth might be possible, qd 43-tooth could be harder to find unless you have one already.
My '69 T100 is 46-tooth qd rear and 19-tooth front. Having discovered some earlier T100's had 20-tooth, I'm debating the change ... I'd only make it if I had the primary apart for another reason, but there's then the obvious possibility I might have to pull the primary apart again to change it back.
I'm afraid I am using the standard 24/25 psi tyre pressures. The tyres seem Ok, not soggy.
Nevertheless, they're at least contributing to the problem you're experiencing. You should be using at least the Avon-recommended pressures: 2 bar (29 psi) front, 2.2/2.3 bar (32/33 psi) rear.
Looks like I need a wider rear rim whatever I do
If you increase to WM3-equivalent 2.15, 100/90 rear becomes an another option; personally, I wouldn't bother with a modern 4.00-width.