I gave BA customer services ample opportunities, they have said that I can't take it any further and that it was the end of the line with them with nothing else they could do and they refused to do any more (I have all of this in a recorded phone conversation). The train ticket was a bit under £140, so not a huge amount, but it's enough for me to want back on principle.
On the day I travelled I asked for what I was told in writing from the BA staff at LHR, but was given nothing and was told that everything I needed was all online at ba.com and to get home and not to worry about it. The agent even suggested how best to get to Kings Cross (tube instead of Heathrow Express as it was easier to do with my bags).
I have no idea about my refund amount, I have asked how much this would be, and been told the customer services don't know and that they can't find out but that it wouldn't cover the cost of the train. How they can't tell me what my refund would be is proof of how un-integrated the BA systems must be! They did offer me a BA voucher for the difference but I explained that I didn't have any travel plans involving BA in the foreseeable future so that offer would be no use. So to answer your points:
(a) my train fare amount, nothing more
(b) they verbally refused to do any more to help me, I did give them ample chances to settle and they point blank refused.
(c) I am, on principle! The MCOL was completed after the BA customer relations person told me they wouldn't do any more for me other than say sorry for being told the wrong information (I have this apology in writing from BA, which seems like an admission of guilt to me)
It's not too late for BA to change their mind, it's one click on the MCOL to say I've got my money... but I don't fancy calling Customer Relations again, I don't think I could stand to hear the on hold music/announcements for another hour!
Thanks