You might try photo-etching. Messier, but very accurate. If you use dry film photoresist (Amazon item) you can expose the film with UV (several minutes of direct sunlight will work) “develop” (clean really) with a mild caustic solution (1~3% Sodium Carbonate) and etch with Ferric Chloride. All of this is available on Amazon.
You can put blue tape onto wax paper and laser cut that. Peel off the wax paper and then use the blue tape as your template. Make sure you account for laser kerf with your cutting vectors unless you don’t need that precision.
EDIT: You might be able to use the wide laser masking “tape”/film that’s next to the Fusion laser; put it onto the laser sticky side up and cut that as your layout template. Remember to flip the image if you do that.