I got to fix this issue in the field last year myself when I believe I was under inflated and hauling a decent sized log on the forks. And it was my second time out with it. Wrap a ratchet strap around the tire and tighten it to set the tire in the bead, then air it up and release the strap. The loader will lift your front end for you, and I THINK the 3pt CAN lift the rear end if you put a log or something under it, though maybe not with filled tires.
After the initial panic subsides (I was quite new at this) you just deal with it and move on. I was able to get it good enough to get out, but there was crap in the bead that wouldn't let it fully seal so I was leaking as I was driving out... Then took it to a tire store and had tubes put in the front tires. No problems since...