Update, and a happy ending (touch wood).
Collected the car from TM Motors yesterday. They fitted a brand new MAF and crankshaft position sensor (I had purchased second hand ones but not had time to fit, took them down with the car but they refused to touch them). This fixed the rough idle, acceleration problems, and the warm start problem. They only started working on the car on the morning of Mon 6th Feb and had already phoned me by midday saying those three probs had been solved.
They went over all of the electrics and traced the battery drain to the central locking pump. They offered to replace but are obliged to use new/warrantied/approved Merc parts so it would have been £542+VAT. I declined this, now they've pinpointed the cause I can look for a used unit on Ebay. I never ever would have found this, I would have had the car crushed out of frustration first. So this is the bit of work I'm most grateful to them for.
Even though my battery is 6 months old it was slightly below the recommended CCA and failed their battery diags, so they fitted a new, suitably powerful unit.
They MOT'd it for me and it failed needing a drag link assembly (whatever that is). So they replaced that, put it through again and it passed.
The aftermarket stereo had been wired in by a blind gibbon (i.e. the mate that sold me the car) so they sorted that.
All of this wasn't cheap, but I had said "don't give it back to me until you've found/sorted everything on this list" so they must've spent a day labour just chasing the battery drain around the car.
The car is a completely different animal now. It actually launches at traffic lights. I seem to live near lots of sets of traffic lights where just after them the lanes merge so he who gets ahead first claims the lane. I'm stunned by how quick it'll pick up and take off when the lights turn green.
They spotted a couple more things that might need attention over the next few months, do I'll book it in again in the Summer to get those bits sorted.
Hurrah for TM Motors!