'92 XTZ660 Tenere cold start problem

[lowuk]

I'm using this bike as my only transport at present. The bike starts Ok if its been in the garage overnight, even if there's been a frost. A bit of choke and it will fire up.
The problem only occures on days when I've left it on the drive a few hours before starting it, in a cold wind. Half choke is not enough. It fires up very briefly on full choke but does not catch and run, repeated efforts lead to a flooded carb, and flattened battery.
I had the bike looked at by a local bike shop with plenty of experience in older jap bikes. They took up some slack in the choke cable, checked that the choke worked, and adjusted the carb.
A cold windy day today and the same problem again. Fortunately holding a fan heater to the top of the engine for just a minute, it started with no choke!
The bike shop are willing to have it in again, but apart from checking the valve clearances and compression , they are wondering what else they could try.
I wonder if it could be a split in the carb-head rubbers, but it runs so sweet once it is running.
The weather is getting steadily colder and I dread being caught somewhere away from home and the fan heater.