Go to the Miami airport and start by speaking to the folks at the Delta counter (I believe you are new to ASA) and tell them you are trying to find out about local parking as a commuting crew member. They should be able to point you towards the local office of the folks incharge of employee parking.
It will most likely cost you a monthly charge as ASA will only give you free parking for your crew base.
I was able to get an employee parking pass for a one time issue fee (not at MIA). I asked an airport employee “where do I get the parking permit?”, and he pointed me to the office. Just say you work for delta/delta connection, play dumb and don’t surrender too much info and you may get hooked up foe fwee!