[JohnKSa]

The movement of the guide rod is as you described. It just comes slightly out of the assembly notch.

That is perfectly normal behavior. The assembly notch is just there for assembly and the guiderod doesn't stay in that position for long once the gun is assembled. During normal use the guiderod drops down slightly--after the slide moves backward more than about a tenth of an inch after the first time after the gun has been assembled. If we think about how the barrel tilts down during the normal slide operation it makes sense that tilting action pushes the guiderod downward too since it's directly under the barrel. After it's been pushed down that first time, it stays down.

...the jams are rounds stopping against the feed ramp or less often a stove pipe.

I hate to say it because it's such a cliche, but my best guess at a cause is a grip related issue. Especially since the gun works for you but not for him, and especially with the types of malfunctions you describe. Stovepipes being included in the symptoms makes it a classic case.

I didn't know that holding the trigger down while removing the slide made a difference with the NY trigger mod.

The normal trigger spring pulls backward and upward on the trigger bar. The backward pull holds the trigger back against the connector ramp which (since the connector ramp angles downward) keeps the trigger bar from drifting up and possibly interfering with the striker. The NY spring pushes upward but applies no backward force on the trigger bar. That upward force can cause the trigger bar to move upward and with nothing to hold it back against the connector ramp it can drift forward and upward and catch on the striker. That prevents the slide from coming forward during the removal process. Squeezing the trigger applies the backward force required and allows the slide to be removed easily.