Hi, and welcome to OpenStreetMap! Since you requested a review, I looked over your changes. Looks great overall! I think you made the right call here in adding access tags rather than deleting altogether. That's because if it's completely deleted, there's no information about whether the trail is unmapped but legal, etc. In this case, I think to further discourage use we could remove the name tag as well.
On a related note, I see there's an "Elk Meadow Shelter" feature too. If the trail is off limits, is there some other way to access the shelter? Or is that closed too?

Thanks for your contribution, and again, welcome!