What do you suggest using to cut core plugs out of recoil pads?

I make a simple cutter, sharpened tube cut on the lathe. Lubricate with oil when you cut the pad. I find having several sizes helps. You can grind the plug small enough to cover with leather but I find that laborious, I cut a smaller sized plug from a scrap pad. Multiple ways to get good results.

you can get a set of cork borers from a lab supply company or maybe ebay.

I use a .375 H&H case. Sharpen the case mouth with your deburring tool & lube with petroleum jelly. Twist the case (I glued the case into a small block of wood) & don't apply too much pressure.

To hold the plug in the pad I use small amount of Pliobond or Barges cement.

To me, this looks much neater than cutting an x in the pad face or putting an unplugged hole in the pad if we are talking non leather covered pads & allows easy removal & replacement of the pad w/o buggering up the pad face.