Anybody know if maybe this has a reverse thread nut? Sprinkler valve handles are shot & I can't get them to budge. Don't want to completely break them off & there's not much left! And obviously it's underground so I can't get a good look at them.

I don't think so. I'm in the valve business and change handles frequently. Can't say ever noticed them being reverse threaded.

PB Blaster with a small cheater bar won't work on that first pic?

I've had to put a 6-point box end wrench on mine before until I got em loosened up. Would suggest the same. Make sure water upstream is turned off if possible in case something breaks

Probably corroded with a locking nut.

Either try a rust penetrant or a nut splitter. CRAFTSMAN Automotive Nut Cracker CMMT14117 at Lowes.com

I'd probably get a proper bit and socket for a small 12 or 18v impact DRIVER. Not a Impact wrench like you remove lug nuts with, a driver you drive deck screws with. I'd soak that in Kroil or PB Blaster and in 12 hours, I'd pop it with the impact. The trick is to go 'easy' with the impact. I like to attempt to provide enough pop to break it free, but not so much that I strip the hex head off of it if it doesn't give. I'd give it a shot, and then more blaster, impact, blaster, and then if that didn't work, I'd apply a little heat. Not much, you'll melt the seat and everything around it. Just enough to get it warm and encourage movement.

I believe other methods will require you to use that rusty handle as a means of holding the stem firm. I fear that this will result in breaking that handle off. It's fine is that's the last resort, but I'd probably go impact first.

Appreciate the recommendations. As Jason said I worry the handles are going to strip off pretty easily. And of course the gd nut fits no standard or metric socket. Afraid I'm stuck with a vice grip as my "wrench"

Try a 12pt socket. It's probably metric. Lol. I don't know I just find it tough to think it won't fit something.

Job Done! Sort of. The handles broke off when trying to break the nuts free, but I was able to vice grip the crap out of the handle nub and the nut to get them off.

Turns out it was just a 3/8" nut but they were so corroded the sockets just rounded the corners off.

Big box stores don't sell replacement handles so I ordered two different sets off amazon. Neither fit. I drilled out the holes in the smaller set to make it fit & got new nuts from Ace Hardware.

The threads on one of the bolts are all but shot and the nut comes loose with any more than hand tightening.

I would have fired my ass long ago if I was charging by the hour...but hey it's done