Joe,
I agree with drilling a hole to the hinge and using gorrilla (or other) urethane glue. That stuff will expand and find its way into the gaps. Used the some method you are describing with that profile. Just drill the hole drop in the glue, and then cover the hole with some wax paper and clamp so it can't back out. I've yet to have a hinge come loose with these glues. Also, I've used it to fix some profile landing gear areas and it held under the abuse I put it thru ... lots of abuse!