Right on Jeff! Based on your comments, I'll give some more info about the hikes I know about.
The scrambling might knock out Picketpost and Battleship. The latter I've heard has a decent amount of, and the former I can definitely say is locally well known for it. Battleship is also supposed to severely test someone's fear of heights, similar actually to Angel's Landing in Zion NP but without chains to hold onto. Vulture Peak has a decent scramble to reach the top as well of about 240 feet, but is otherwise a nice, challenging hike to consider.
I hold that Sunrise Peak checks off all the necessary boxes for consideration though. It's challenging and long enough but not too much, though the last quarter mile to the top is very steep and care should be taken on that part. It's not a scramble though.
The dirt road to Harquahala is rough, but I'm not sure I'd say 4×4 is an absolute necessity – plus it's no more than 2 miles one way. But even if you're not comfortable driving it, you could park just off the 60 and add about 3.5 to 4 miles round trip. However it's already at least 10 miles as is, with over 3300 feet of elevation gain.
Wrightson is an underappreciated classic, and when I was thinking of SE Arizona hikes to mention, this is the one that made me want to think of six. It checks off every box, the roads are paved, no scrambling, a very challenging but very satisfying summit hike. I'm honestly amazed more people don't hike it, and in some ways I like it better than Humphreys even!
Miller Peak is actually the only other one I suggest that I've done. It takes a dirt road to get there, but I don't recall it requiring 4×4. There also wasn't any scrambling while still being a solid challenge. If there's one concern people might have, it starts very close to the border. However I didn't see any suspicious looking activity the one time I did this one.
My understanding about Carr Peak is it may take 4×4 to get to. Rincon Peak is supposed to also take a few back roads to get to, but not sure about 4×4 being required. I think any vehicle can make the other two, and both Silver and Chiricahua Peaks aren't supposed to have really any scrambling either I don't think. I'm definitely hoping to knock out the latter sometime this year, and some of my friends are very interested in Carr Peak as well.