You're offering an awful lot for $10.00 if you provide edge bands! Sure, why not? But it would be a PITA because the affordable stuff is tongue & groove, you would have to use a jig to cut the grooves, then cut those floopy tapes to exact lengths, and then miter the tongues and corners. How long would that take?
One option is to get something like a Keencut or Fletcher-Terry table top sliding cutter that can make super clean cuts on the edges of Gator. Hand made cuts will never make the grade. Call the bare Gator edges a "look." If nobody's complaining about dings on the edges of fomecore, maybe they'll love the sexy gator texture, which can argued to be in the same ballpark as carbon fiber, sorta. You could hit the edges with a blast of clear acrylic spray for about 1/50 the cost of edging. Ooh! I'm gonna try that! Wait, meltdowns... Maybe water based, Polycrylic comes in cans, too. Maybe just the same coating used on canvases...