My after action report:
Initial assembly of the saw was done well, except for installation of the clutch side crank seal, which was installed too deeply. This cause the inner bearing race to tear up the inner seal lip and lead to an air leak.
I replaced the seal, and the saw was still running weird. This was probably due to two factors: Bad fuel line/filter, and bad carb nozzle check valve.
I immediately assumed that I had installed the crank seal improperly again, so I removed it and installed yet another new one. The method that I used to remove the seal was the "drywall screw" method, where I tapped a drywall screw into the crank seal and yanked the seal out with pliers. This led to the next issue.
After installing the seal, I fired it up and immediately the saw started acting very strange again. Again, I suspected the clutch side crank seal. When I removed it, to my surprise, I found that the plastic bearing cage had completely disintegrated. What I now realize is that I probably damaged the cage with the drywall screw that I was using to remove the crank seals, and it subsequently melted down.
Next, I tore the saw completely apart again, replaced the bearings with OEM Stihl bearings, took care to install seals properly, and reassembled. Frustratingly, the saw was still acting weird. I tried a number of things, including different fuel filters, multiple vacuum/pressure tests, spraying carb cleaner while running, etc. I began to suspect that the case was leaking from a crack around the steel bearing seat insert.
After being distracted by that idea for a while, I decided to try another carburetor, one from my 044. I put it on, and the saw was still acting strangely. Then I decided to reseal the cylinder base with Dirko, replace the fuel and impulse lines, and replace the fuel filter. After doing all of this, I put it back together with the 044 carb and it started running well. Then I put the original carb back on it, and it was running badly.
That's when I decided to punch out the nozzle and test the check valve on the original carb. I found that the nozzle was not actually holding pressure, and I swapped the nozzle for one from a junk HD carb that I had in my box. Threw the old carb back on and it was running even better.
I now believe that the cylinder base re-seal was unnecessary. I think that I was experiencing multiple issues at once with the carburetor and fuel filters, and that I never had a good fuel filter and a good carb on the saw at once until I put it back together after re-sealing the cylinder base.
So to re-cap: I initially had a bad crank seal, a bad carb, and a bad fuel filter. Then I fixed the crank seal issue, but still had a bad carb and fuel filter. Then I replaced the carb, but still had a bad fuel filter. Finally, I replaced the fuel filter and fixed the original carb.
Go figure. I definitely learned on this project that it's worth it to go all-new OEM on the fuel line, impulse line, and fuel filter from the get-go. I also learned to check the carb nozzle check valve sooner, rather than later.