I've used about about 5 plugs since removing the studs....
Never again!
Ouch!!! Sounds to me like you put in the wrong screw type and the wrong screw length too. You don't wanna use self tapper types and you do want to use proper made for the purpose screws. IMHE
I have a 2WD tractor with diamond pattern turf tires. Certainly not the best tires in general for sloppy conditions and tantamount to useless on snow and ice fwiw. I have used tire chains for two seasons with great results save the installation and overall experience/adjustment hassle. The chains I have are expensive ones with cross hatch cutters on the outside bite surface, sort of like a barbed wire fence but chain and they dig in well. Pretty hard to get the tractor stuck even on 20 degree incline fwiw. I use it in the wintertime with lots of weight on the front and back with plow and blower combination.
Without traction assistance on slippery stuffs, with these tires, it will get stuck in its own tracks. The chains work great but they are a PITA to put on and to adjust and to keep in place. Ultimately, they will shift and be eating at your metal parts including your fenders and 3pt hitch arms. And you will be hassling around readjusting them which ain't no fun cause the tractors sitting on one part of the tire/chains so that won't move so you have to move the tractor to adjust the chains 2-3 times.
So I just did some experimenting/tried koldkutter ice screws tonight. This is after getting the tractor stuck on a flat concrete garage entrance apron just a week ago. Literally, the tractor got stuck right there. I didn't have the blower on the back and the plow on the front unweighted the back and it just sat there and spun. LOL
So I put ice screws on the center of the tire three wide. The Diamond pattern is offset so 2 diamonds offset then one diamond at the center then two then one and so on and so forth. Used 1/2" [woulda preferred 3/4 but I had em layin around from motorcycle ice racing] koldkutters, one screw in the center of each diamond. Put in with a rachet screwdriver applying pressure as I put them in and no predrilled holes.
Went out in the 2" deep sloppy wet icy slime with screws on the drive wheel and chains on the other. I didn't need the differential lock to get me out of anything. The screws dug into the frozen ground/ice/snow mix and I went where I wanted. Slope or no slope. Same as I do with my ATV with the screws installed. Same deal different app. None of the screws came out... why would they? And no the tires are not flat... you have to use the right length of screws for your application. If you use 3/8ths screws they may come out due to the shortness of the thread but 1/2 and 5/8ths and etc.. are very secure. 3/8ths are actually very secure and I use those on the ATV cause the knobs are shallower.
My opinion so far is they work great. Before you go listening to anyone tell you sure.. on ice but not in powder snow...... try em for yourself. Powder snow does not stop my ATV at all. It cuts through and those screws bite. Worth their weight in Kold. LOL