We had the same quandary - a single ticket but a change from BA to AA. The website initially suggested a 2.5 hour turnaround but (mindful of previous immigration experiences) we went for the next flight and a 5 hr layover - we ended up with 4 hours to spare!
It is good that you are aware of the requirements, as I don't think we were explicitly told to collect our bags (which had been booked all the way through to Hawaii) and we could have unwittingly gone through immigration and not bothered with baggage reclaim. It was all very smooth and baggage drop is fairly obvious once through customs. Compared with previous immigration experiences it was fairly quick.
We arrived in the TBIT and departed from T4 - the procedure takes you outside and back in to T4 but once back in both terminals are connected by a walkway so you can wander between them. If you have suitable tickets, or one world status, I would aim for the Oneworld lounge in the TBIT over the Admirals Club lounge in T4.