As I don't see the head's rim, I assume it is behind the hole in the matting through which the head protrudes. Is that right?
Yes, that's right. The sink mount consists of two foam board layers beneath the window mat, with circles cut to make an interference-fit just tight enough to keep the drum head from rotating. The foam board touches only the aluminum rim and two layers of conservation board separate the foam board from the plastic drum head's Sharpie-Marker autographs, so I'm not concerned about the chemistry. The customer knows they'll fade from visible light exposure over time, anyway - we've had that conversation several times before.
When the customer specifically asked for a 3-dimensional checkerboard mat, I said "Oh, sure, we can do that, no problem" before thinking through the labor involved. I've made several inlaid checkerboards previously, such as Gregory describes. In the old days, manual cutting of the squares was a touchy task, but the CMC makes quick work of cutting perfect squares, so they fit together neatly. However, in this case, having to glue each black square onto the solid sheet of white required very careful placement. A skew of just a couple of degrees would be quite noticeable.
I included an up-charge of $40 for the checkerboard, but it should have been more. To make accurate placement easier, I cut a template mat with a diagonal zigzag 'staircase' design. Also, I ran the checkerboard-design cutting file with the blade barely scratching the surface of the white mat to lay out the grid. The template and the scratched surface made placement easy enough, but those provisions would not have been needed for an inlaid assembly.