Looking for any information from recent cruisers on this, we are on the May 14th Pride of America cruise and I can't find anything about overnight parking.
It's about $11 each way through Lyft. The drive took roughly 7 minutes each way. Uber will cost more and a taxi will cost even more than that.
The counter time can vary a lot depending on which company you go rent with. Budget FASTBREAK is pretty quick because you get head of the line privileges.