My experience is that the GS has to be intercepted from below in order to
couple (also true for the 225). Also, it seems like use of the pitch toggle
while in approach mode will prevent the AP from capturing the GS.

This has happened on multiple occasions when given a late vector to
intercept, along with an altitude change, while already in NAV or HEADING
mode, with the APP mode armed. In other words, using the toggle switch for
pitch on the AP master panel while in APP mode seems to prevent the AP from
sensing and capturing the GS. This has been true for ILS as well as GPS
(LNAV/VNAV or LPV) approaches.

My only thought was to not engage the APP mode until the final altitude is
attained for GS intercept.

So, the main question is: with a King 200 AP, does the use of the pitch
toggle switch on the master panel while in APP mode negate GS tracking? How
about the CWS?
Does a switch from APP to NAV and back to APP then allow GS tracking?