If they’re coplanar you could use a surround frame to hold them in place as you glue them to each other, but somehow I think maybe you’re not talking coplanar.
here’s a thought, engrave an area on the back for gluing a sort of exposed spline (I guess it would be called a decorative spline if it were on the front).
Now you’re in for reverse aligning issues. If only you knew someone who was good at that?
I still think I’d use a kerf-corrected frame. You can arrange your materials “face down” and backside-masked so there is zero gap between the back sides (cut profile works in your favor here). Then you can just flood the keystone kerf gaps with glue from what will eventually be the back of your finished piece.
Wipe off excess… let it dry in frame, then remove it and flip over, demask and clean up if necessary, and I bet you’d have a nearly perfect end result.
Of course, I elected not to do this and instead changed my design to have an integrated frame (yellowheart) and made it a kerf corrected flipmated inlay:
it just seemed a lot simpler than trying to rig up so many layers of hackery. Your design needs may be different, and a border might not be acceptable. You’re the artist, what you say goes