The extension to our house is built to earthquake standards, so there are 10x10 posts and beams everywhere. We can't find a path to feed the 12AWG to the subpanel. If we go down, we just run into the same problem on the ground floor. Can't go up because it's a flat roof. Any ideas?
Also look into the Conduit wiring method. This allows you to put up to four circuits (or even more with a wire size bump) into a single hole/pipe, instead of only one or two cables.
This works because you are fitting individual wires into a pipe, instead of a sheathed cable containing multiple wires, so you don't have the bulk of the sheath, packing and grounds. All the circuits in a pipe can share a ground, and if the pipe is metal, it can be the ground.
This is worth confirming, but in my experiences, all makers of engineered lumber has install guides to direct where and how big holes can be made in their products. These are available on line at the manufacturers website. If I knew the brand and the material in question I could look it up, but....
Put a Crown Molding, Decorative Strip or Cornice around the ceiling and run a cable behind that. Conversely, the baseboard(s) can be removed and any wiring can be run behind that, at the bottom of the wall(s).