You need to make a to do list and pin it on the wall

at least you can see you are making progress.
So on some of your list-
Gas to petrol switchover, what you see is normal,

When it is below 3 deg I lock it in petrol only mode until she is warm,
:thumbdwn:There is no switch back function when you run out of gas on these systems

on switchover you need to keep the revs up (above 2000) or she will stall, I blip the throttle in neutral before I move off to switch it over.
:thumbdwn:The hard switchover issue - it should not switchover when you accellerate, but should switchover when you lift off (providing you have a TPS input to the unit). Also the gas isn't there yet is true, there are two gas solenoids, one before the regulator (energised when power is applied to the control board, the second is the one that releases the gas to the stepper motor valve or the manifold. after the second solenoid the gas is at very low pressure so takes a couple of seconds to get through the pipes.
On the gas tank fill, it sounds like you are overfilling it, you say the capacity is 55 litres, if so your tank size should be about 80 Litres. - I have a 100 Litre tank and will only ever get 80 litres in it. (something to do with a space for vapour?)
The fact that you have rough running and stalling from cold would tend to indicate a manifold leak, until you sort this out the gas system will not run properly as a low vacum will affect the gas regulator (which is a vacum demand system). I spend a lot of time getting the manifold seals right on mine.
lastly the Gearbox, I had exactly the same issue on mine, worst when I was on a motorway going on a long uphill stretch or when towing. Leave it shut down for 20 mins and all good again - Turned out it was the fluid getting too hot, A filter change and a change to synthetic sorted it, never to return.
I know it is no help, but when I got my EX 18 months ago (from ebay!) it was awfull to drive, the gas system would just stop working, it felt like it had square wheels, electrical gremlins (including mirrors), in fact most of what you have and then some.
You just have to deal with each issue in turn - But I still drive mine listening for problems
Keep the faith!
Jim