I'm aware of the horrendous passport queues but I'm not sure about this scenario. I'm planning to fly from NAS to LHR via MIA later this year (NAS-MIA will be BA miles on AA and MIA-LHR will be paid but I'm hoping I can link the PNRs so my bag get checked all the way through to LHR?) and I'm trying to figure out what flight times to book. Last time I entered MIA I was stuck there for ~4 hours. For this particular flight, would I have to clear immigration at MIA or do I just go through flight transfers where the queue would be much shorter?
Programs: AA EXP 2MM, Lifetime Platinum, HH Gold, SPG Gold, Travelers Aid JFK Volunteer
There is no such thing as TWOV any longer in the USA. All passengers transiting through the country, regardless of final destination, must clear passport control and customs at the first point of entry. Most passengers also must claim all checked luggage before clearing customs.
HOWEVER, in your case, you are in luck! Nassau offers US FIS Preclearance, so you won't have to worry about it on the outbound. You will clear passport control, customs, and agriculture in Nassau, then arrive at MIA at a domestic gate and be dumped directly into the terminal/departures area. So, you will be able to proceed directly to your gate for the LHR-bound flight.
And no need to "link" your PNRs, as you can thru-check bags even on different carriers and different PNRs. Just have copies of both itineraries handy when checking in at NAS (and pray for a competent and friendly agent).