While I'm an epoxy repair novice myself, I recently had to do a fairly significant repair to what I thought was a small rail ding, which turned out to be much larger than I thought:https://drive.google.com/uc?export=view&id=0B-VYU87hIeSSOTRlczdzYUlXMjQ
After sanding it down, it looked more like this:https://drive.google.com/uc?export=view&id=0By31olSZJTuteE5ZVlJyc2xDWVE
And it was spongy under the entire area about 1cm in from the edge of the outline. It needed to be cut out:https://drive.google.com/uc?export=view&id=0By31olSZJTutM2dBclYzb2lOY0k
I then filled it with 2 part epoxy and Q-Cel (3M Micro Bubbles will work too), sanded that down, did the laminate layer, more sanding, then a 'hot coat' (at least as much as one can with epoxy). I'm not gonna lie, it was a lot of research, sourcing materials and work; but I'm happy with the result.
If the box is moving 2mm, you might have a bunch of crushed foam with voids under the laminate like I did. Your best bet is to sand down to the glass, then you'll have a better idea of what sort of repair you're looking at and it won't screw anything up if you need to take it to a shop.
If the fin box needs to be re-seated, you're probably best taking it somewhere for repair if you can; they'll have all the equipment and materials to do in a few days what will take you a couple weeks after work and on weekends trying to find places that have clear epoxy and weird fairing compounds.
With all due respect to chipmunk, I don't know how he can so confidently assert a plan of action without having seen the damage in person.