Update:
On the ground, with the engine running or not, it works OK with distant stations (people calling LHR etc).
There is no evidence of ignition interference - well not at sea level air pressure.
The #2 radio is slightly more sensitive than the #1 radio, but that's not an issue and in any case one would expect it to be the other way round if there was a cable/antenna issue.
Swapping the radios doesn't produce any meaningful data because I can't replicate the issue on the ground in the first place. But clearly there is nothing wrong with either radio or either antenna as far as sensitivity (gain) goes.
The interesting bit was the airframe bonding. On the TB20, there isn't any... well there is one strap to the rudder (I know because a couple of years ago it came right off) and that one measures fine (below 1 ohm). The ailerons measure ~ 10-20 ohms which is obviously not bonded (and they have static wicks) so that is just the conductivity of the bearings etc. The flaps are well grounded and have wicks.
The elevator is the best bit - it measures over 10 M ohms to the airframe!! It has two static wicks but clearly they will be useless except for the elevator itself.
So, apart from the flaps and their wicks, the parts of the airframe which have wicks are poorly connected to the airframe.
Yet AFAICT this is correct for the TB20/GT. It never had an elevator strap, from new.
I will get an elevator strap done and see what that does.