Thanks for the replies, Folks.
Lacking the right tap, and not keen on spending money on something that really shouldn't be "broken" (a brand new Colt barrel), I improvised.
I took an old FSP, used a fine file to taper the threads a bit (about half its length but still enough bite to avoid cross-threading), and using the front sight tool and some "cutting oil" I ran it all the way down by the "half-turn and back-up" method. I then used CLP on a Q-tip and cleaned out the loosened parkerizing gunk that seemed to have filled in the threads a bit in the first place. I ran my makeshift tap a second time and re-cleaned the threads.
After that a new post went in with slightly more than finger pressure resistance, and it assembled without incident. All is well.
RRA223, that method may work for you too. If you don't have an extra FSP, you can probably do this without filing anything in that yours is already assembled and moves. Take it apart (remove the detent & spring) lube it well and run the sight post all the way down, clean, repeat. But use a real front sight tool -- the bullet tip thing won't do it, and needlenose vise grips will surely mess up the post.
Cheers, Otto