Thanks a bunch for the further info an encouragement! You guys' encouragement will likely end up costing me the 'idiot fee' assessed when a failed DIY project is finally taken to a pro to unscrew, LoL...

(I appreciate the tip on calling Mike at Ocean Air - I'll do that tomorrow, and see who he can recommend, just so I have some idea of what that option looks like.)
So, it sounds like:
1. Open things up and remove the original mast box. (there's still the matter of that white plastic bit surrounding the part of the box that broke - I have no idea if that is part of the board, or part of the original track, nor how big it is and thus how big of a hole it'll leave behind if I can mange to remove it in a semi-finesse-ful, non-catastrophic manner.) I also need to figure out how far back the top sheet is damaged, and cut that out. (as well as prepare the edges with the proscribed bevel)
2. Determine how much gap there is between the new scary hole in my board and the new mast box. Depending on the size of the hole, either fill it all with pour foam, then route out a new slot for a snug fit of the new box, or if lucky enough to have the scary hole be a fairly decent fit for the new box, proceed directly to step 3. (It sounds like the advice is to NOT just pour-foam the new box into an oversize scary hole though, huh?)
3. Epoxy/q-cell the new box into the snug slot. (recessing the top surface of the box by the thickness of the intended topsheet layup)
4. Do a 3-layer layup to entomb it all in. (Whether glass or CF yet to be determined. Also, find some means of preventing epoxy from filling up the brand new mast box... That'd be a hoot to find that full of epoxy in the end, eh??)
5. Excavate down to the (hopefully empty) box slot, and clean the topsheet edges up up so that I can actually get a mast base down in there in order to sail.
6. Finish in some manner that meets my very low aesthetic standards, but that hopefully doesn't create a slick area upon which I try to dance while tacking. (I've got some Re-Deck, which I've had very limited success with, but which I guess is a tiny bit better than a baby-bottom-smooth surface.)
Please let me know where there are holes (literal or figurative) in my plan.
Thanks!!!