Man, I've seen that kit (never built up of course) and I didn't realize that you had to paint the checkers yourself! That sucks! I would have thought that it was a decal for sure.
I agree, cutting that many squares would be such a pain, I don't think it would be worth it. I think I have an idea that would at least minimize the amount of cutting you would have to do.
First paint the entire area white. Next I was thinking of laying several (however many it takes) strips of tape, cut to the proper dimensions, and making a thatch pattern with them. Lay the vertical pieces first, then lay on top of that the horizontal pieces. Leave a space between the strips that is equal to the width of the tape. Once that was done, you're left with a thatch, but you will have to cut out every other square (on every other row) to make a checker pattern. Paint the exposed area red and you should be left with the checker pattern.
I hope this works for you, or at least gives you some other ideas.