97 VW Golf 2.0 P0341 error code

I changed the timing belt on a 97 vw Golf 2.0, 5 speed. While doing
this, the distributor cap hold down clamps broke (rusty) while double
checking TDC. Got a used distributor that looks like new.

Anyway, when I tried to start the car, would not start. I figured I
had gotten the timing belt wrong. But decided to check the
distributor. It was no longer pointed to the TDC mark. So, rather
than redo the timing belt, and move the intermediate shaft, I simply
installed the distributor pointing to TDC.

The car started and ran, quite smooth. However, it threw and check
engine light. I and a few others, assumed this was just due to the
ignition timing being so far off when I tried to start it.

I went ahead and changed the clutch and trans (no reverse) while I was
still up on blocks. That seemed to go reasonably well, for how
difficult a job it is. Also changed the water pump, earlier before
the timing belt. Just mentioning all this for completeness.

Finally got around to connecting an ODBC tool and found the P0341
code. Cleared it and went for a drive. Seems fine, but, sometimes,
at idle, the engine wants to stumble, when starting off.
The check engine light will come on when that happens, a P0341 code
again. Then it runs fine, until the next time.

Some searching seems to indicate this could be a bad distributor, and
not just the cam timing being off.

I should mention that the timing belt marks to not align "perfectly".
The cam is off "a hair" from "perfect", but way less than 1/2 a
tooth. It has been my experience, doing other timing belt on other
cars, that a 1/2 tooth indicates being off one tooth on the crank,
relative to the cam. The marks, do align exactly as the old belt did.

So, where am I? Do I chase a bad distributor, or hassle with trying
to get the timing belt marks "perfect"? My experience has been that
if cam timing is off "by a tooth", the engine will simply not run, or
run very, very, poorly.

Thanks.