Is there a way to determine whether the problem lies IN the distributor?
Your timing light reading has already shown you that there is a problem within the advancing mechanasm.
This is NOT timing belt related.... even with a tired timing belt.
The belt has either slipped a cog tooth, has broken, or is still working!
The rotor returns to stop point when I twist it -- does this mean the advance mechanism is functional?
Yes and NO........, and to a point only.
At the distributor, we are seeing 1/2 of crankshaft angle. IOW, a 10 degree crankshaft error, will show up as only 5 degrees at the distributor.
Using 5 degrees, you can see that this becomes difficult to determine the actual amount of error........., and is exactly why we strobe timing degree markings.
I'll clean up the distributor springs/weights and belt tensioner today and check the belt and pulley timing marks.
I'd recommend that you do one only at a time by focusing on the distributor first.
Once you get that corrected and the timing set, test it, and see what the progressive advance is doing!
Then change out the timing belt and tensioner.
P of E.... "process of elimination".... one item, and one item ONLY until you isolate the problem.