You could fill them, but use something easily reversible. I like Durabond Topping Compound. This is a gypsum based 'final coat' quick drying, light-weight filler. It will get you what you are looking for, a level surface under your artwork, and if you need to get at a bolt or two, you could easily remove it again.
Alternatively, skip the filler entirely, print your artwork on polycarbonate, and layer that between the cp surface and the plexi, retained by your buttons in a nice sandwich. Then you can just pop your artwork off/out whenever you need to. The polycarbonate is tough. Printed vinyl, or paper is not, and always seems to get damaged when you open up the control panel 'layer'.