What about duct seal? I've seen folks seal distributors with it on off road trucks. I have used it to seal holes in the firewall, but never tested it in water, let alone warm water for an extended period.
https://www.homedepot.com/p/Gardner-Bender-1-lb-Plug-Duct-Seal-Compound-DS-110/100212441

WARNING: I have never tried this, so you might end up with a huge mess trying to clean it off the antlers, or it could leak and you could end up with an even huger mess.

Edited to add: That cooler is the perfect size. Gotta love that!

Last edited by cwh2; 01/30/20. Reason: write more stuff