I've had good luck using two-part clear epoxy, available in any Home Depot/Lowes/hardware store, to fill small voids. There are some kits that come pre-packaged in a dual-tube syringe, or the cheaper version has two small squeeze tubes in a blister pack.
You will want to test this with some spare caps, of course, but once you drill the hole for the LED, just use clear plastic tape (or similar smooth surface material) to seal the hole on the "face" of the keycap, then pour or drip the epoxy into the opening from the back. Use a small needle or pin to coax bubbles out of the epoxy.
Should stick to the cap material just fine, especially if you let some excess flow out on the back of the cap. Be careful, though. Fumes are highly toxic (cyanoacrylate is nasty stuff...), use mask and safety glasses, plus disposable gloves. Excess resin can be cleaned up with alcohol, but it sets up quickly, so put down some wax paper on your work surface to catch drips.
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On a note about the capslock LED through solid caps... is there an off the shelf material that could cure in a small drill hole on the key top that would refract the light somewhat? Well, i realize there's probably tons of products that would do this, but what would do it very well? Is this a thing? has GH vetted such a mod? Do I know how to use the search bar?
I have so many questions.