To be honest it would be best to check with the consulate re the TP run. The extra legs may complicate it a bit if your ultimate destination is Heathrow.

As far as TPs are concerned, BA does have a fairly standard procedure for granting a 14 day extension. So if you can't do the Bucharest legs it does give you a chance to slot in a quick TP run to make up the missing TPs. I would not bank on BA showing sympathy for something which is not under their control, so to speak.