The 5th and Mission Garage is a short walk from the hotel.
http://www.fifthandmission.com/home.htm
It is $23 for 24 hours (no in-out privileges) - from the 4th St. side, it couldn't be more than a 10 minute walk to the hotel. You could unload at the hotel, go to the lot and park, and then the next day, pick up the car, go to the hotel and load, and then off to SFO you go. It is a huge lot and you will find parking, even if it is on the 77th floor

Just park on the 4th St. side.
End of story, problem solved, money saved.