BUE-MIA-SFO should be your best option. I don't know why ppl complain about MIA (from BUE), if you take the early fligh on AA, you will avoid the crowd. I have Global Entry, but I'm just arrived this morning on AA900, the ETA was 4:20 and we landed around 3:45am, we still have to wait until 4:05am because Customs does not open until 4am .
We were the first passengers arriving on MIA, I had to use the regular US Citizen line (no kiosk) because I was with my mom (she is a visitor), I was out of the airport by 4:40am.

I had a similar trip 5 weeks ago and it was the same, both lines (visitors and us citizens) were short, but that time I did use my GE