I have had some success with stuck screws or screws that have rounded out hex drives by taking a "small" dremal tool and using the smallest cutting disk. I use the disk on a piece of junk metal to wear it's diameter down to that of the diameter of the screw head. Then carefully cut a slot in the screw head. You will probably go through several disks. Then, with a Flat Blade screw driver and hard force into the screw to keep it engaged, you can some times get it to back out. Spraying the screw with a good penetrating oil such as PB Blaster several times over 3 or 4 days prior to extraction ". If this fails, then you are pretty much left with drilling out the screw. Use a drill that is about 0.020" under the "Minor" diameter of screw. Google the Major and Minor diameter of the screw you are working with. Then use an "Easy Out" screw extractor. I have pasted a location at Amazon that has several sets. You will need one that goes that small. I have found that the key is to put a lot of force into the screw to get a good "bite" on it. Also, last thought. Make sure the drill bit is aligned with the screw shank. This is kind of difficult laying under the belly. If possible, have a friend help by looking at the drill bit shank and telling you "left, right, this way that way" so you are aligned.
https://www.amazon.com/s?k=ezout+screw+extractor&crid=2UCNEWB5AMJQ0&sprefix=ezout%2Caps%2C171&ref=nb_sb_ss_p13n-expert-pd-ops-ranker_6_5
Best of luck,
-mark