The area around the base of the Pinalenos (Mt. Graham) is mid-level desert, and likely to still be very warm at this time of year. That said the drive up to Mt. Graham is enjoyable and offers a look at one of southern Arizona's "sky islands"
I've never been on either road you mention but my quick research shows that they could be interesting adventures depending on your expectations. Personally I'd wait for cooler weather to do my exploring but you've gotta work with the time you have.
Good luck and have fun!
Jackson Cabin RoadBlack Hill Backcountry Byway