On two different occasions I have changed out mower turf tires for ag lugs and couldn't get them to seat, even with a strap.
My local tire shop bailed me out both times, and didn't charge me anything. I think they even refused payment so that they wouldn't be held liable for tires they didn't sell. One of the guys told me their trick was simply the combination of a big tank on the shop compressor, and a clip-on tire chuck that would work without the core in the stem. Pop the tire, pop the core back in, inflate to rated pressure. Took about as long for them to do as it takes me to say.
While I don't have the big compressor, I did pick up a clip-on chuck to experiment with. I'd also be interested in making one of those bead seater tanks with the big dump valve that hooks on the rim and blows in the gap. But I'm also willing to bet this little trick would work about as well. Definitely have to keep it in mind.