A common problem is that the tire slips a bit on the rim, pulling the inner tube with it. The valve experiences kind of a shearing force due to the movement between the inner tube and wheel.
To avoid this problem, fix the inner tube (patch or replace) and always check the tire pressure before operating. Chances are your innertube is bad at the place where the valve comes in. Of course, when changing the inner tube, check the inside of the tire with a rag in case there is some piece of metal or glass stuck in the tire that caused the leak in the first place. (You sound like you know what you are doing, but other people may read this forum after searching or whatever.)
I've read here on this forum that some people put water in the inner tube to add weight to the tractor. I don't know if slime would interfere with that, but you may want to avoid the slime to keep that option open in the future.
Personally, I hate slime due to bad experiences with bike tires (it makes a mess if you ever have to deflate the tire).
One more thing. I've changed two inner tubes. I found the tires kind of hard to take on and off of the wheel without good tire irons. After the first one, I ordered some tire irons from amazon that made the job MUCH easier. Soapy water helps, too.
--McKenzie
You are correct it does have tubes so back to the days of patching. I haven't had to do that for some time. It didn't even dawn on me that there would be tubes in there. lmao... Well off to work I go.