It sounds like you have it all correct.
The only real comment that I have is that whenever you sell House A, the $250,000/$500,000 Principal Residence Exclusion gets a bit funky because you rented it out and then moved back into it. The exclusion will be prorated, based on the time it was your Principal Residence compared to your total ownership time. But you won't need to deal with that until you sell House A.
