Welp, tried a patch. Didn't take.
I've got to say God bless a decent jack (mid-range harbor freight, low profile) and a pretty kick@ss Bosch impact driver.
I had the tractor jacked up and wheel off in about 3 minutes.
I found the puncture, just a tiny thorn looking thing, certainly from mowing over too big a stuff in the back field. Jammed a patch in there, which held long enough to move the mower deck out of the barn, put the blade on, and move the tractor back into the barn. Overnight, the flat was back. I had some old slime (moldy and disgusting) that I tried, unsuccessfully, to put in, the pump was all funked up and it hosed me down with that stink, so I got some new slime and that appears to have done the trick, at least for one night so far.
Now it looks like my steering fluid is back to leaking out from under the steering wheel. Not sure why or if it's still leftover. Steering was a hair slow to respond but I also haven't checked the fluid since I refilled it after busting the hose.