Heya Byron, I was on the team that was rebuilding Paul's earth berm shed last year and some videos were posted of that work, linked below. Pounding the logs into the hole with the excavator got them to sink several inches with the sandy soil. My own plan is to use a steel bar once I get a hole to 42" depth, and compact the soil down, then add landscape fabric to the bottom, which will keep the 6" of gravel I add for drainage in place. Then another piece of fabric on top, which will hold the borax, DE, and wood ash mix that is added to limit fungal growth due to any remaining moisture in the log which drains once installed. Then the log goes in, wrapped with something to keep the soil off, but the end of the log is not wrapped- just the 36" of the sides which will touch soil. That way the log drains into the 6" of gravel and once dried out should remain that way. Especially during the build, my concern is rain getting the site wet and having that wet soil against any wood for the days it takes to dry out. So wrapping the sides should help while the roof and then umbrella are installed.
If you can drain the umbrella to an elevation that's lower than the post hole depth, you should be set for rain, and as long as the water table stays several feet below during spring runoff/rain season it should be all good. I bought some 1" wood dowels to cut out "logs" to build a scale model, and you can then cut out furniture with paper to move them around to get a feel. My own property is pretty flat, I will build where I have a bit of drop as I plan to dig 4 feet down, so I want to french drain the umbrella perimeter to sunlight below that. Was also planning to add an earthship-inspired greenhouse on the south wall to use as a buffer in winter and try growing warmer plants using some techniques from the book The Forest Garden Greenhouse. Might work for you as well, add a few months to the growing season and you could run sink/shower gray water out through it to the outside. Perhaps compost the toilet Humanure style.