I have done this job once fairly successfully
I agree with all of above by Mark. Make sure the new hole is not too much bigger than fin box and use
slow hardener. It can be a bit of mucking around to get the depth correct, especially as most router bits will not go that deep. There are some router bits available that will go that deep (I have one that will cut about 80mm deep- can't think of brand). The inverse pattern following bits are just the best if you can be bothered spending the money (but won't go as deep as you probably need
www.carbatec.com.au/pattern-bit)
The multitool is a great idea.
Routers are good, but can have a habit of grabbing. I clamped a few guides onto the board prior to routing out my busted fin box.
The chinook box I used had a big cavity in the top side of the box (see photo 2 in link below). (I filled this cavity up with foam and set it with resin and let it go off prior to inserting the box into the board.) The "slope" on the top of the fin box fitted the deck profile of my board very well. If the depth and "top slope" of the finbox does not match the slope of the deck, it is worth getting this sorted- cutting, sanding, shaping carefully. This will also dictate how it is finished on the deck/underside of the deck as the top of the screw sleeve (and hence the box around the screw) ideally needs to be flush with the deck.
Draw on some accurate guide lines for getting the fin in straight (and making the router cuts nice and straight) and make some off-sets of these to make sure they can still be seen when all the crap and tape is in the way.
Interesting that Eva Hollmann goes right through the board with the box and then seals from the deck side
www.boardlady.com/jppowerbox.htm This would go a long way to minimising overheating of resin around box and some of the depth/profile issues mentioned above.
As Eva Hollmann says, use a nice long fin and measure accurately to the rails (prior to glassing in box) and tape it in place until the epoxy goes off.
Good quality blue masking tape (the $20 per roll stuff) is your best friend on these jobs.
Nice board by the way.
Good luck
Clarence