I live in Punta Gorda, at least in the winters, and there is only one haul out yard- Punta Gorda Marina, located inside the 41 bridge on the Peace River. But access is sometimes limited due to the shoaling channel leading in to it.
Don't even consider Riviera Marina south of town. It is a total dump.
The other marinas are probably full, but Laishleys' Marina would be the first to call. They do have moorings outside of the marina on the Peace River that may have space.
Much further away there is an inexpensive haulout and dry storage yard on the Caloosahatchee River NE of Ft Myers near La Belle- Glades Boat Storage. There are also several marinas along the Caloosahatchee. One, Port LaBelle Marina advertises $6/ft which would be cheap enough for a few months of slipping but I don't know if they have space.
David