I disassembled the jet and burner, blew out the jet with butane and added the washer (it's a size 1). The washer is not thick enough to make a difference, the poker still tilts up and contacts the top of the flue. The gas tank was filled and then allowed to empty.
In fact, it may be counter-productive, as after reassembling the burner assembly, I can't get it to light at all -- the flame stays in the smokebox and won't pop back; if I cut back the gas slightly, it pops back into the flue for a moment and then goes out. This is true regardless of the setting of the burner collar.
Well, it makes a nice desk ornament...
UPDATE 5:45PM EDT: I disassembled the works again, removed the washer from between the burner assembly and the boiler. Also renewed the teflon tape that was used -- in fact, had been over-used -- on the jet to seal the thread, also added teflon tape -- again, sparingly -- around the jet holder when re-inserting it back into the burner assembly. Note that tape was used by the factory when assembling the jet into the holder, but they used far too much and there were parts of it in the holder itself. The tape around the holder was my addition, as it was pretty loose in the burner assembly without it.
Now the burner lights normally. I don't have the opportunity tonight to bench-test the loco (not without incurring the wrath of She Who Must Be Obeyed) to see if the popping problem persists, so a full test will have to wait for tomorrow.
Yes, I understand completely that there are likely too many variables for me to pinpoint what went wrong here (and how much of it was self-inflicted), but my strong hunch is that the washer solution that was suggested for the burner misalignment is a waste of time. Next thing to check will be whether insulation makes a difference.