Opportunity is missed by most people because it is dressed in overalls and looks like work. - Thomas Edison
Burn a screen and print the marks on the board directly?
Use a piece of glass to keep it flat. If you are not registering the films to each other than the depth of the glass is not going to change your accuracy. We have had a similar setup for years and have had the same piece of film below with no wrinkles.
I made a white Formica top, layed out the grid lines then took my router with a pointy bit and cut my marks leaving a narrow score line. Painted the lines with several colors of paint for reference let it dry then took a razor and scrapped off the excess paint.
Use Letraset?