Thanks for the interest and encouragement Michael 😊
Update: on Monday I fired it up with a remote fuel supply into the carbs and it ran well.
So I refitted the air box, reconnected the fuel lines, pump tank  and filter but when I tried to start it yesterday there was a leak from one of the fuel lines. I'd used the original jubilee clip but using the correct fuel pipe fasteners cured it.
I managed to get it running again on all 4 cylinders and it ticks over as well.
The next problem is the indicators have packed up. This has already happened once and was fixed with a new correct spec relay. I'm guessing in putting it back together I've disturbed the wiring, the connections are not great so I'll need to trace that through again as the relay is under the left side panel which could have been affected when I refitted it

I've ordered the Mitas from Demon Tweeks in 3.50x18 size. Meanwhile have taken the old Roadrider off the front wheel. What a struggle! I had to use my home made bead breaker for the first time since making my Tiger wheels tubeless (below). The tyre was like iron, which is not surprising - when I looked at the date code it's 16 years old. I think it would have held the bike up with no air at all it was so stiff, and this probably contributed a lot to the shimmy problems. The task wasn't helped by the Akront flanged alloy rim, which seems to be deeper than the chrome rims I'm used to. Fortunately managed without nipping the tube or damaging the rim so am just waiting for the postie with my new tyre. I think there's room under the mudguard for it.....

I suppose I should now check the date code on the back tyre although it (and the front) wer performing fine when the bike was a solo. Although only in the dry of course. And I don't want to repeat that fight any time soon.

More woes with this project.
I got the carbs back on and tightened the clips with the new screws but the thing still wouldn't start and would only fire using Easy Start.
My mate diagnosed stuck floats from debris in the old fuel pipes.
Tank tap and pump can be ruled out as I was poring fuel directly in to the carb fuel rail.
I've also fitted a new fuel filter as a matter of course.
I removed the carbs and took them over to my friend on the 650 Interceptor when we had a brief but lovely few days of great weather.
He serviced them again and blew everything out with compressed air.
Over the weekend I've been struggling to refit the throttle cables as I can't seem to get enough free play.
Anyway they're on now.
I've got some new correct style of  caps for the deeply recessed spark plugs so we'll see if the thing can fire up now?

25 psi was much better. I still did get a shake when hitting a bump but it quickly subsided. I'm amazed how much difference a couple of psi makes. I'll probably try 24 but am reluctant to go lower.

I've also decided to go for a flatter type tyre - a Mitas H-03 in 3.50x18 size. I've used Mitas on various classic bikes and they work well. The ideal would be the Avon sidecar tyre but apart from being unavailable they only do a 19" version. The old Safety Mileage would be another option but again unavailable. I suspect the Mitas may wear more quickly but given my limited usage not a problem.

Out of interest, the manual suggests 16 psi for the front tyre - but this was back in the 1960s when tyres were stiff and fitters were tough.

Now the good(ish) news. I filled in a query form on the Avon (now Goodyear) website and was very surprised to get a phone call in return from a very helpful chap. He stressed that he was calling rather than emailing as nothing he would say could be construed as "advice" for obvious legal reasons. Anyway, he was very helpful regarding tyre pressure / load combinations and it's clear that I've had the front tyre overinflated - and it still is, probably, at 28 psi. The unladen weight on the front wheel is 86kg - let's say that increases to 120 fully laden. According to my chap, this would correspond to a pressure of 21 psi (the lower limit to stop the tyre coming off the rim). I'd be very uncomfortable at that so will try the effect of 25.

I have been trying to work out the effect of front tyre pressures and it has struck me that lower pressure equates to a bigger footprint which would act to increase effort required to rotate around the steering axis - exactly the same as the effect of a steering damper. Like trying to steer a car with flat front tyres and no power steering. So I think I'm eventually on the right tack(!). Hopefully I'll have another short test today at 25.

I must say I've never bothered much about tyre pressures on solos, taking a starting point for most as 28 front, 32 back although these are for bikes weighing 180 kg or so. I seem to remember the Tiger liked 42 at the back but it was a big heavy beast.