I'm working on the same idea. I was going to try filling the pop cap with silicon gel and placing the ring in there leaving the back exposed. I'll let you know how it turns out. Epoxy might work too but might not be as clear. They are cheap so I'd just replace the cap and ring as a single unit if needed (need a molex connector to make that easier)

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Just frost the cap to hide everything. Staring directly into those LEDs isn't the most pleasant anyway, and you can see each lee individually once it's illuminated.