Have you tried lower-tack masking? It comes in various stickinesses.
As a proof of concept you can try reducing the stickiness by adhering the masking to a cloth and removing it once or twice. Each time it should come away a bit less tacky.
What about sealing the photo paper with a waterproof coating? You may be able to wipe the residue off safely?
In general you can reduce smoke residue by cutting via multiple passes at lower power and higher speeds. You may be able to get an acceptable result that way?
It’s also been shown that elevating your material can reduce both flashback and smoke residue on the bottom surface of your cut. Rigging something up to hold your photo above the crumb tray might assist things.
I had some success with a vacuum tray reducing smoke residue but never quantified it nor tried it with something like a photo.
Maybe some things to try in here?
Edit: ah “sprayed with fixative” I guess you tried sealing already. Cool that it worked, bummer it’s not viable at scale.