I managed to remove the tire, and with Grandpa's help, we eventually got the remains of the bearing off.
It took nearly two weeks for a replacement tire to be found and mounted on my rim, but this past week I was able to pick it up and begin the process of reinstalling it.
Grandpa suggested a fix that he has been using for many years - replacing bearings with wooden ones made of tree limbs. He brought over a suitable diameter of birch, which I peeled and drilled a 1" diameter hole through.
This fit nice and snug. But of course, there was another issue - I could no longer find the washer that held the wheel on the axle!
Once again, wood to the rescue. A slightly larger disc of birch was pressed into service and so far is holding... We'll see how long it lasts under real use though.
In the meantime, I was able to flip the trailer back onto its feet, and roll it to the top of my ramp down to the sawmill. Soon I will load it up with slabs and get them under better cover.