I just want to close the loop and thank everyone who provided their input.
We will be heading down for our annual visit to see my folks in Green Valley in a few weeks. We can always get a good feel for mountain conditions by looking at the peaks from my parent's back patio in Desert Hills.
Additionally, my parents serve as fine "conditions reporters" as they'll have been hiking in the area for weeks before my husband and I arrive.
Thanks to those of you who suggested other mountains, although some (like Wrightson) are already included in other plans and others just aren't what we're looking for. (You know - this porridge is too hot...this porridge is too cold, etc.)
At any rate, it sounds like the surest option is to register for the Whipple Observatory tour, but see if we can't hike there (or at least hike part of the route). Strikes me as a lot of hassle to have a fun day in the mountains with my folks.
There are plenty of other peaks in the area not so encumbered by red tape.
Thanks again to those who replied!