For these sorts of things, always ask here before making decisions if you can, there are some very knowledgeable people on this forum and you can normally get good advice within an hour. I'm not sure you did the right thing here since European legs are usually easier to sort out (and there were thousands of empty seats out of LHR yesterday). Depends on the details I guess, which aren't provided here. If this was a BA shorthaul service then that had a waiver allowing changes (and you would have gotten the same waiver, plus additional protections, if it was a single booking).

BA193 was caught up in the ATC issues, and left late London very late to DFW, due to the manual scheduling of aircraft out from the UK. Therefore your flight BA192, returning to the UK, was delayed by 4 hours and 5 minutes on arrival (it left about 5 hours late so she did make up some time en route). Had you been on that service you would not have got any compensation due to the ATC failure, no question of that. I'm not sure of the ticketing conditions on your fare but strictly speaking BA can insist no changes unless there is a 5 hour delay, which there was on departure, but not on arrival. Now depending on the fare basis and whether it was 125 plated, then it's possible BA would give you an involuntary refund on the downgrade to Economy, but if it's treated as a Voluntary change then there may be no refund, again depends on the fare basis details. You should certainly apply for a part refund, but you won't get compensation, just any Right to Care expenses. If it was 001 plated then that's best asked in the AA forum.

If you are going to book separate tickets, there is a big factor about the 5 hour rule, so separate tickets really need a 7 hour separation, or an understanding that the second booking is disposable, which in many cases is in fact the case.