Echoing the others. MIA immigration can be horrendous.
Sometimes you get segregated and go through your own (horrible) area with one slow moving queue. If BA or AA arrive at the same time, you might be queuing with up to 500-1000 cruise passengers!
And other times you're queuing up in the main hall with most of Central and South America getting grilled as to their intentions!
Neither are great. 1h45 would make me a bit twitchy. Surely the Cessna can adjust to your schedule?