something that I realized while doing this is just turning on wireframe for the model in object data-> viewport display->Wireframe [x]
then while in edit mode you can see the vert you want to snap against the model instead of switching back and forth.
Shift + axis while moving it will also exclude it so in the linked image I have the x axis excluded in snapping to vert.
You can also use wireframe from overlays drop down. Add it to your quick favorites. Also Ctrl+Shift+Tab for snapping option and Shift+Tab to toggle snapping. Also once you start the move/Rotate/scale you you can hold shift then press and hold middle mouse button drag along the axis you want to exclude. If you want to constraint to a single axis just press and drag middle mouse button. This can be easier and faster for some people.