Any wood used is only needed for a temporary backing plate.
If I was to do this job, I think I would work from the outside with a 12:1 bevel and make a backing plate out of 3 or 4 layers of 1708 cloth and then attach that to the inside with some thickened epoxy after it cured. This will give you something firm to work against.
Then following the instructions on West System website, I would lay up multiple layers of glass, again using 1708 glass. The outermost layer would be the mat side of the 1708 and it would be a little proud of the transom. Once everything is cured and solid, the real fun begins with sanding, oh glorious sanding. Bring the glass down even with the gel coat. and then begin to feather the existing gel coat. You'll end up with a big dimple with both the patch and the original glass exposed. Then fair, and fair and fair. Eventually, it will be smooth enough.
When it is smooth enough, time to put on the gel coat and sand and buff it out.
A common assumption of first time glass repairers is that only one coat of fairing compound is needed and if it needs more, then you screwed up. This is not a good assumption. It will take several coats of fairing compound and the creation of a lot of dust before the hull is ready for gelcoat. Also, West System and microballoons can be used for fairing, however, this often leaves pinholes. A compound like Total Boat Total Fair or Interlux Watertite fairing compound will leave a smoother final finish.
Get a good sander and lots of sandpaper.