The wood is apparenly only intended a backing plate. Its task is to hold the screws (think of it as a giant nut and washer). Being loose is not a problem for that purpose. (Once the fiberglass is restored, and the screws are tightened, there should be no wobble).
What seems to be an issue is that the laminate might not have been strong enough, so the repair may need to add some more thickness.
Also, I would make sure to cut back the old laminate rather far, so that the connection between old and new is not in the highest stress area.
Here's a suggestion how to proceed:
1 Cut away several inches around the repair.
2 Bevel all the edges. (The ideal slope for that is 1 in 12.)
3 Take cardboard and cut and fold to make a mold that fits into the inside of the channel (you might need two pieces so you can fit them in). The cardboard should extend a bit underneath the old material, just to keep it in place.
4 Shave the wood so it fits inside the cardboard
5 Place the wood
6 Precut your fiberglass and mix the epoxy
7 Coat the cardboard with epoxy on all sides and fit into the opening.
8 Coat the cardboard and edges of old material with epoxy
9 Add a layer of glass
10 Squeeze out excess epoxy until glass is wet out
Add the other layers the same way until done.
For the cardboard I would not use corrugated, because that's hard to coat fully with epoxy. If you mix only a small batch of epoxy and let it cure after step 7, even thin cardboard should work (cereal box or from back of a paper pad).
For the new laminate, you should precut the first layer so it fits the entire repair, even the edges. The next layer gets a little narrower, so it fits part of the edges. When done, there's going to be a bit of a rough area around the edges of the repair where all the layers terminate. If you did things correctly, you should be able to grind that area flat, once the epoxy has cured.
To add strength, you should add two final layers, that build up a thicker laminate in a "stair step" fashion, with the two steps at equal distances, the first starting say an inch or so beyond the mast support. The idea is to gradually increase the wall strength, to distribute the stresses gracefully. (If the new layers overlap the joint from new to old, they would help reinforce that as well).
Since you are new to epoxy: I recommend you build a dummy first, do a few layers over a cardboard mold. That should give you a feel for how this works. Better to be able to throw out a not-quite perfect first attempt than to be stuck with it inside your boat.
Good luckl!