There’s a few questions in here and I’ll try to tackle them each. Please let me know if I misunderstood.
First, we can’t recommend a third party insert; it could cause all sorts of havoc.
Second, wine glasses are probably too tall to engrave, even on their side.
Third, the engravable area is 0"-0.5" from the top of the tray. That means if you remove the tray, the part you engrave still needs to be where the top of the tray used to be.
If the black rectangle is the 1.5" tall tray, then you can engrave the green arrow amount. If you remove the tray, you can’t engrave the blue arrow amount, but you can put something (like a 1.75" spice jar) in there and engrave the top of it.
EDIT: Yes, that means you can engrave 2" thick material, not 1.5" like it says in the specs. Two inches for everyone!