Help needed on the best way to core drill a thick, soft plastic sheet

A question for the hive mind.

At the shooting club I go to we have bullet catchers that use a 35mm thick EVA sheet as the front of the bullet catcher. When these are shot out we core drill the center out, 118mm, and just replace this core with a new cast round.

The issue is that as the drill cuts into the sheet, the EVA starts to melt and binds the bit.

This works, eventually, but is hard on the drill clutch and wrists!

Has anyone got any experience with these types of materials that could help us with this issue.

The cut portion needs to be cleanly removed, to the correct size, so the new center can be added. Removing the plate entails completely emptying the catcher that is full of EVA granules, so the sheet needs to be cut in situ.

Many thanks,

Not enough information, Question 1 what are you using as a core drill? #2 what RPM is the drill # does the core drill have any set to the teeth to allow the hole to be larger than the body of the drill.
Annular cutters work great for things like this but are expensive, and just like a deep hole saw they should be run at a low RPM , High velocity air blown around the cut will help to blow the chips out of the hole the chip granules get between the drill body and the base material which causes friction and heat
A carbide tipped hole saw would work well I should think since the teeth protrude outside of the body but still need the chip removal A mist cooling set up like used on mills would do well also just plain water and air possibly 100 to 200 to one ratio this will cool as well as blow out the chips. Others may have better ideas

Make a cutter from a tube of the correct diameter and grind a shallow chamfer on the inside. Run at a fairly slow speed and it will sail through. You could even cut it by hand rotation back and forth like this. To make plugs make another tool ever so slightly larger with the chamfer ground externally.
Depending how thick it is you could also cut it with a circle cutter with a razor blade. Jigsaw blades for foam are the same, just a very sharp knife.
Otherwise find a genius to create an ultrasonic cutter.

EVA - https://en.wikipedia.org/wiki/Ethylene-vinyl_acetate

Think foam kneeling pad, flip-flops (the non-electonic kind), foam garden slipons, etc.

I would think the removal of material requires a sharp thin edged tool with no teeth, a thin wall tube sharpened to a razor edge that cats more as a punch, perhaps with a small rotational force back and forth, but as you said, it will grab and heat will build up and then it gets worse.