Beulah? Hop, skip, and a jump! I'm in Cheyenne!
Anyway, have you ever hunted moose? Did you get the type 1 (any) or type 2 (antlerless)?
Though I have never hunted moose in that area, I have hunted elk. On and around Shadow Mountain and Blacktail Butte. Which surrounds Antelope flats. On up to Lower Slide Lake as well.
Moose hunting is like lope hunting, you drive around a lot, jump out and shoot one. Th4ey are not skiddish like deer or elk. Thay are very mellow. You will see some, you will get one.
9/4-10 is likely to be pre-rut. With the 10th-on getting more into the rut. Not that that matters much with moose. I've never drawn a tag yet, but I'm in and around them all summer (ATVing) and fall hunt (archery to rifle).
This area is north of Jackson up hwy 26 / 89 to Moose Junction (like that name?!) The butte on the east side is Blacktail Butte. You are still south of Moran Junction. And north of the elk refuge boudary. Lots of parking for camping in the area.
Get some topo maps of Jackson Lake. It's a start.Hope this helps.

p.s. Call the G&F in Jackson.