Sounds like your bike doesn't like you...

I use a regular 10mm socket on a wobble extension(1/4" drive). I have seen pics of the frame tube joint on our bikes and it seems like Kawi can use many variations of a gusset to reinforce that joint. I ground off a small amount of that gusset to give me better access but it should also be possible to use a box end 10mm wrench from underneath.
To do that I would grind off the heads of the stripped fasteners and remove the skid plate-you should be able to grab the nubs of the damaged bolts and work the out-use penetrating oil and some heat if they are really stuck.

 

Yeah, and previous owner overtorqued everything
Box end wrench won't fit, I've tried. That metal bulk/extrusion at shift shaft is too close to nut for box end to slip on. Is yours a 2nd gen klx? Mine's a 2006.

My only 10mm socket is a deep one, but I don't think a short one will make a difference. I'm trying to find a thin-walled, shallow, 10mm swivel socket online and not having any luck.

I hadn't thought about using a grinder. I don't have one and I'd probably screw something up since I've never used one. But maybe one of my neighbors can help.

 

You must have some pretty beefy wrenches because that's the first time I've heard of that problem. You would have better luck using a thinwall socket with a wobble extension.