Sorry to hear this. If you are arriving more than 3 hours late you should be entitled to claim UK 261, which will give you around GBP 600 per pax. Keep your receipts for food (anything other than alcohol)., hotels and transport as you should be able to claim those back too (ignore what BA told you on the phone, thats rubbish).

Dont be too disheartened about going on TG; they would be my preference over BA any day. Not quite up to QR standards, but still a good product. If you are in J, you will get a flat bed, direct aisle access, a decent feed and usually a very friendly/warm crew.

Not sure which Taxi company you are using in BKK, but most of them have whatsapp or failing that, Line. Message them through there and you should get a quick response.