If 12:30 works, we'll aim for that. We'll spend enough time in BA's LHR lounge waiting for our connecting flight to want to spend time in another lounge.
Not an EU citizen, so fast track immigration sounds good. We'll stop at the check-in desk. (It would be nice if US global entry had reciprocity with the EU.)
Chaos does not sound good, but so long as there's space in the overhead bins, we should be able to cope. We haven't had a real problem with priority boarding with oneworld for a while, so it's not good to hear PRG boarding is a mess.