I've been out there more than a few times. When I really want to punish myself I ride the scenic road in the park. My poor husband usually pulls the trailer up that one! It's about the only time I ever get to whip up on him! I also like the hikes there but so far as I remember no mountain biking allowed . I've got Tuffy liners between tube and tires so no flats for me, knock on wood. We're in the St. Louis area so don't make it up there as much as I'd like to. If I didn't worry about cars around the trailer (parts of the Alton to Grafton section) I'd ride from the Arch up to PM and back.
Boy, I sure don't envy you that hill home, either. Whew! Do you ever do the Fun Club rides? We do the Tuesday night rides (Arch to the Chain of Rocks bridge), the Wednesday night rides at Creve Coeur Lake and some of the bigger sunday rides. Pulling the baby sure puts a dent in both my road and off-road riding but he's worth it.