The "advantage" of Miraflores is that you can use the coastal road for part of the trip to/from LIM - it has no lights or real intersections. To downtown I imagine you're stuck on roads with lights pretty much all the way. Cab drivers are good at "navigating through traffic", though.

As far as hotels in the airport, there is a Ramada across from the terminal in LIM. Nothing really of interest around LIM.

I also used an award to get there - booked about 6 weeks prior, with ample off-peak availability almost every day! (30k in Y). Actually, the DCA-MIA &vv legs were a lot more tricky than the MIA-LIM &vv legs.

Note that AA operates the A300 on the route, and you may get an aircraft that has the high-density Caribbean-service seating (no headrests, limited recline). F looked horrible - hello 1985. The plane on the way back was marginally better. Also, you may want to try for LP - LanPeru, who also has a LIM-MIA red-eye (leaves LIM at 00:20 or something vs. AA at 23:10).