OTOH, I have been through FLL on cruise days, and would rather undergo Cuauhtemoc's torture, I think.

OP, domestic to international you will already have checked in, received your boarding passes, had your documents checked and had that marked on your BPs, and merely make a gate change. The map below may offer some perspective; your connection will largely depend on your flight's timely arrival.

It appears a number of ORD-MIA flights arrive in the D gates, and the CUR flight may also depart from the D gates, according to recent records. You may be able to make a very speedy connection.