The plexiglass idea works very well.
I used to have a large sheet of plexiglass that I had attached hex grid to the underside of for use when playing AD&D. A sheet for a “sliding glass door” replacement panel is a standard size that you can get at a home improvement store and measures about 33" by 75". I think I had paid about $25 for the last one I bought (circa 1997)
With the plexiglass, you are going to want to also get some small felt “feet” (the little self adhesive felt disks) while you are at Lowe’s and put those on the corners, and a few along the edges. That will help preent sliding, and will protect your table top.