Butyl type sealant sounds good, but like you said, you'd have to completely un-crimp.
A very thin, slow-drying glue, will be carried by capillary action to where it needs to go, without un-crimping. In a different lifetime, I repaired pottery and ceramics. One way to repair a clean crack, was to tightly hold the two pieces together with tape or rubber bands, than apply glue to the crack, and capillary action would draw it completely inside the crack. I used a proprietary archival epoxy that was the consistency of water and took a week to cure. And, it was expensive, so I don't recommend it. Instead, I'd try original super glue (not the gel type), which is also the consistency of water, and should wick in just fine. Go all the way around the rim, and maybe do one or more repeat applications, after it dries.
