Done! (Still have to get some secondary regulators, and I'm missing a tap handle, but otherwise done!)
I decided the hinges would be on the lid and the collar would stay in place rather than lift with the lid. But I didn't affix the collar to the freezer; I just put some rubber foam weatherstripping around the bottom of the collar and gravity holds the collar with lid attached in place. Then if I need to, I can just lift the collar/lid off, and more importantly, the freezer is in no way permanently modified so the warranty is still intact.
Here's the weatherstripping I used (the collar and lid assembly is upside-down in the pic).
Here's the finished product minus a tap handle:
I installed the taps off to the left not only because I liked the look, but because one more keg will fit in there, so I can drill another hole for another faucet if I want to in the future, and I couldn't have centered four and then added one later and still have everything centered.
Obligatory Perlick showoff shot: