Generally people is reluctant to give straight recommendations but you can find some by searching using the search box top right. Since you're in the USA you may find convenient to use "AWCI online directory" that gives a list of certified, accredited USA watch repairers.
Well, I have finally found the "true source of the problem", and I feel equally elated and embarrassed
The problem is that I replaced the setting lever screw after I replaced the barrel bridge, when in fact the setting lever screw must be replaced before the barrel bridge. Doing it in the wrong order "works" but it will make the oscillating weight slightly foul the head of the screw and it will make it impossible to remove the stem without the setting lever detaching from the setting lever screw.
This mistake I won't be doing again!