Can't help you with a 37ft...we did stay in the campground with a 23ft TT many years ago. If I remember the roads are a little narrow with tight turns through the loop. There may be a few spots accessible for a big rig. The low hanging tree branches were gone.

On the NPS.gov website none of the campgrounds for Yosemite show a maximum trailer length over 35 ft. I'm sure that's due to the narrow roads and tight turns within the campgrounds. That being said there are usually a couple of sites where you may need to go the wrong way (with ranger permission) on the loop to get to a site. We've done that at a couple of 35ft maximum state parks.

We find with our 38FT 5th wheel it's better to stay outside the parks at a big rig friendly private campground and drive in for the day to tour a National Park.

Stayed at Crane Flats a few years ago with our 30 ft TT, quite a feat getting the trailer into the campground due to trees, tight turns, etc. and then could never quite get the trailer level due to the slope in the campsite. I don't think I would even want to track our current rig in there and I certainly wouldn't want to do the drive over Tioga Pass. Have you checked the National Forest camping on the SE side? I don't remember how far the June Lake area was from Yosemite, it might have been closer to Mammoth Lakes. We found several larger sites in that area that were much more accommodating to larger rigs.

As I recall when we were researching the visit, staying on the East side of the Sierras was less expensive and also a lot less crowded.