Welcome to the forum.
The first thing I will say about the Green River in July is "bikini hatch". Second I will say avoid the 'A' section. If
you must fish this section then do it very early(at or before sunrise) until the floaters start, and later in the afternoon to avoid the recreational floaters. It will cost a little more but in my opinion you are better off fishing the 'B' or 'C' sections, somewhat fewer fish, but they are bigger. And with the light Winter and dry Spring to this point, the hoppers may start a little early and be going strong by this time. Big Browns on big dries or streamers is often the game on these two sections.
There are a bunch of Guides in the area, here are a couple outfits that have been on the river for a long time that you can't go wrong with.
Trout Creek Flies.
Good luck with your trip.