Modify how far a drive bay opens?

I’m trying to replace the DVD/RW drive inside a primera CD Duplicator

The problem I’ve ran into though is that all drives I find don’t open sufficiently far enough to work in this scenario…

I know the drives are “capable” of opening far enough cause if I just pull on the tray it comes out how far I need it to come out…

Is there some way to modify the firmware on a drive to do this? or is there a drive out there that will work?

I bought an HP dvd 1140i and it doesn’t work. From what I’ve seen I can use all the LiteOn utilities with this drive but none of them seem to deal with the mechanism of opening/closing a drive