The house does not need a soundstage to work at all. Sure, it would have been great to have a large facade in the woods (similar to Cabin in the Woods or Dead Water bayou)... but that's the only benefit it would get. What makes Jason (and other slasher-based houses) great is your proximity to the character, not the setting necessarily.
F&F has not been my favorite venue, but this house uses it masterfully.