The grooves needed in the substrate are hardly more than deep scratches. And less than a 1/16 inch apart.
A real challenge for old eyes and shaky hands.
Ah, but mankind is known as a; "toolmaker" (among other things).
Make something to help.
Imagine a router table, with router and router bit -
Only scale it down for the job at hand -
Make it quick, an 8-month old project thread doesn't need anymore delays.
Instead of a router and router bit, plan on using a Dremel Tool with the smallest engraving bit on-hand at the local store.
Find chunk of wood (a 2x4 foot piece of 1/4 hardwood plywood), start cutting, gluing, finishing - -
And as shown in the before, after, and underside pics - -
A "router table" with a Dremel Tool accessory used as the underside mount.
Not easily seen in the "after" pic - a 1/8 inch hole in the table top where the engraving bit protrudes (0.010 of an inch).
Note: Credit cards are 1/32 inch ABS plastic sheet. ABS sheet is easy to work, you can groove yours, your way.
I just suspect I will be grooving more than one plastic tab.
Plus, I will probably use this "engraving table" for other projects.
If not, it will become a foot stool or lamp table.