FWIW, only Lonesome Lake is in the State Park, Greenleaf is just outside it. Not that it invalidates your point.
It strikes me from looking at the terrain from GE and topo maps that they could expand the south end of the northbound lot by quite a bit, if they desired.
And perhaps as much as some may bristle at the suggestion (including to a degree, myself), maybe it should go to a reservation based system like Baxter. Cut down on the hoards and make it a more pleasant experience for everyone, plus hut guests would be guaranteed access. Guests of the attractions can have their own lot with their own parking pass for verification/enforcement. Yeah, there's a lot of work where the State is involved, but with as this is getting to be more and more of a problem, the question should be asked, is it worth it going to such measures to achieve a goal.