Most people would find getting a pole a daunting task. But this is Idaho, and there's literally a pole store just up the road from me. You can buy anything from fence posts to Class 5 utility poles, the latter of which are expensive - a 25' pole is about $500. But I don't need a gigantic pole, just something to hold the router, a solar panel, and a few antennas. I called the pole company and they have lathed lodgepole pine poles, 7" diameter and 24 feet long, treated for ground contact, for $141. That might be a little on the skinny side in terms of leaning a ladder up against it, but it should do.
Edit: stopped by the place and looked at a few poles they had stuck in the ground. Decided to go with a 20' pole. Burying 4' still leaves me with 16' AGL, and I think that'll be enough - half again as far up as that test pole, and about as far up as I'm willing to ladder. The pole is actually doweled, which means they jam a tree trunk through a 7" die to whittle the pole down to an even size. Larger diameters are turned on an enormous lathe and cost a lot more.
Delivery costs more than the pole, actually, but less than buying a ladder rack for my truck, which is how they'll delivery it. And they'll be able to drop it from the truck right into the hole, so no gin poles needed. They recommend a layer of gravel at the bottom of a 10" hole, then tamped gravel up to about the last foot. From there a concrete collar to lock it in place. Easy stuff, just have to get it plumbed up nicely.
Onto the next task: sizing the solar panel and battery. I order an INA219 I2C current sensor, so I'll whip up a little Arduino data logger and see how much current the hotspot draws on the bench over 12 hours or so. hat should give me an idea of idle current and in-use current.