We are dealing with this as well. Just spent a beautiful night at The Wedge in the San Rafael Swell area of Utah. 6350 foot elevation. Rains make it humid.
Two nights ago we were at Great Basin Upper campground at 9930’ elevation. Senior pass, only $10 a night. We did not have reservations and got lucky.
Tonight we will find something outside of Vernal, UT before heading to Wyoming. We’ve been on parts of WY where you can park on the side of the road. Also, Skyline Drive near Huntington was just under 10K’!