Once cured, the Tamiya putty was very easy to sand down. I used 400 grit paper for that and then went over the entire ship with it to smooth down the roughness left from my previous body-wide sanding, and that worked very well; the ship is now smooth all over. However, this sanding phase revealed my second round of filling wasn't quite enough and a third round is needed.
After sanding, I rinsed off the dust and, once the putty cures, I'll re-apply some more putty, then sand again, then re-prime to see if there is still any gaposis left. I'll fill a fourth time, but that's all the patience I have in me for this project; remember: this is a very old kit.
The next round of filling and sanding will look pretty much like this entire progress report, so the next phase I'll be actually posting is the assembly of the warp pylons to the engineering hull (using glue but installing metal rods to avoid sagging) and attaching the saucer section (using just glue) to the neck. Then I have to fill those seam lines...