Sometimes the the metal clip that secures the plastic tank to the aluminum core can be squeezed tighter using a modified C clamp to clamp it tighter.

If you decide to go the epoxy route I would strongly suggest an epoxy called Fas-Stick #110 made by FASCO in Hialeah FL. This stuff is specifically formulated as an adhesive epoxy and it adheres tenaciously to whatever it's applied to. You're always well advised to clean, degrease and roughen the material as a preparation of course.

This stuff is the consistency of vaseline and when mixed 1:1 by volume it thins a bit to a cold molasses consistency. If you pull the radiator out to work on it that will allow you to get the epoxy deeper down into every crack and crevice, spread it around so there is a larger area of contact and it will hold better.

Here's their web site, I think they sell on eBay also, you can get a small kit for about $10, and the stuff lasts for years sealed up

Fasco unlimited

They make a number of other specialized epoxies maybe even give them a call and they might have a better recommendation