I don't know about lasers but there is ink-jet printing equipment used to
mark products on a conveyor belt. I have encountered these in small
factories here (food industry / canning). This is what puts the numbers on
food cans, yoghurt etc.

I can find out who sells them but me not being lost in Vermont, it's
better to look locally. I know that the ink does not come off with
anything and is food-grade. Which makes me wonder what it's made of.

Maybe you can talk your PCB maker into buying one, the initial investment
being relatively high (but less than $10k if I'm not wrong). The thing
works forever as far as I know (non-contact operation...), you supply ink
cartridges and power, and move the products in front of it.

OTOH, I have used a rubber stamp to stamp numbers into glass boards, and
come to the conclusion that the board must be roughened locally with emory
paper before doing this. Then, the ink stays on and is very hard to remove
completely. The rubber stamp was of the kind used to stamp product prices
in shops (Trodat ?). The ink proved to be un-removable if it was applied
before the last drying bake (after final fluxing - the boards had no
solder mask).

hope this helps,

Peter