We went to the Rocky before the peak season so luckily we could just rock in 🙃 but we did have to book a timed entry for the Arches in Utah. Luckily you found out about it before you went there otherwise it would have been a wasted journey.
That trail inside the park does look a bit scary, I'm not a big fan of heights either, if there are shrubs or trees on the side and I can't see below then I'm a bit better. I just try to pretend the drop isn't there 😅