It all depends on how tight your position tolerances are.
If alignment is key, you’ll need to cut a reference edge or corner to seat your jig in each time. I did something like that with some slate coasters that, for irksome reasons I won’t go into, required right alignment and cutting one at a time. Let me see if I can find it… here we go:
If it were me I’d adapt this technique to get a rock solid alignment before every engraving run (or set of runs).
Edit- I did a similar technique here with one edge alignment on my cheese board:
You can see my alignment cardboard on the left side of the slate in the second picture. While a corner is more securely aligned, it can be done with a single edge.