Mid to late June is the beginning of the monsoon (daily convective weather...at times severe) season in AZ, so you would have be build in flexibility for that. Generally, there is not much of a problem before noon. Tuscon > Deming > El Paso > West Texas is pretty easy. I would consider assembling some sort of emergency kit (communications, a bit of extra water, etc.)
An Archer is a pretty capable airplane even in the higher density altitude areas of the mountain west but you still need to respect it. I think it makes a lot of sense to plan to stay under max gross weight at least for the higher elevation portions.
Winds can sometimes be an issue as well. If the winds aloft are greater than 20-25 kts near mountain ridges, expect a rough ride. My personal rule is to cross any ridges with about 2000 feet to spare if possible. I also tend to follow roads more in the event of an emergency.