Oh, yes.. you did. I wish you did not build your whole entire plan of attack based on one odd video on youtube but this is water under the bridge now. The only reason I bring it up is for the benefit of anyone who might be in your position in the future.
The bad news....
You created a lot more work for yourself than needed be. Most of us do this repair from inside not by removing the outer skin specially that you mentioned the cap is already out. The only reason some people remove the outer skin is to avoid - for whatever reason - removing the cap.
The not so bad news...
Depends on your glassing/gelcoating skills, she might not look the same after you done but this can be avoided - again - by a decent amount of patience and elbow grease
The good news...
Nothing in a fiberglass boat can't be put together with hard work, good supply of patience and good techniques.
There are so many ways to skin this cat, First, forget about tapping the outer skin back in place. This will not restore the original strength to the transom. The edges of the removed skin and the edges of the hull need to be feathered from inside and outside so the new glass is overlapping a good distance on both sides of the seem. There are some formulas to determine this distance but I am guessing a foot or more on each side should do it. The good news is the longer the feather the better and you can't make it too wide so I would feather for 12-18 inches on each side of the seam.
If you already measured and cut the new transom, use it as a backing plate - with no glue or glass yet - only to support the outer skin in place. If the transom is not ready, use whatever technique you like.... Wood dowels cut to size with a bolt and nut through the outer and inner skins to keep the skin in place...... insulation foam sheets from home depot cut to size. The objective is to keep the cutout secure in place.
I would feather all edges before on both sides of the two pieces (outer skin and hull) before securing the skin to the boat.
You got to close to the edges of the transom where it curves and meet the sides of the hull. Make sure you feather through these sides and your glass is overlapping them also. The same goes for the bottom of the hull. The point is that the new glass should spread away from the cut as possible.
You will need a good supply of rags, Acetone and personal protection equipment. Clean all edges with Acetone in one direction and keep folding the rags to a fresh surface and don't over use them.
I am assuming you will be using polyester resin. I use Vinyl-ester as my personal preference and I would advice you to use it also but regular laminating poly resin will also do the job. VE is better though but it doesn't mean that regular poly sucks.
You will need 1708 fabric. Cut it so that each piece is larger than the one before it. You will need about 5 layers on each side of the repair (inside and outside the boat) 5 layer is about 1/4 inch of total thickness. Don't lay them all down at the same time, the generate heat might cook the laminate. Put 2, let it cure and cool then ... clean with Acetone and repeat. Measure the recess with straight edge and see if you need more glass. If you need it use it, it is stronger than filler.
You got to close to the edges of the transom where it curves and meet the sides of the hull. Make sure you feather through these sides and your glass is overlapping them also.
When you are done, cover the whole area... skin, hull.. sides and bottom with two layers of 1708. You are done on the outside
Now, go inside and do the same and build the transom back. The inner skin will need to be cut for that.
Finally, you will need to worry about filling,,, fairing .... sanding and gelling
Some might suggest a simpler procedure and it is up to you to do what you see needed. I am only sharing with you what I would do if I am in your place and if it is an overkill, that is fine be me, Better overkill the repair than it kills me or worse, my family.
One thing you might consider if you see that this is too much work for you is to find a replacement hull. Start with that one and transfer everything from your current boat to that hull. If you think about it, it might be just as much work as doing this one right but you might feel better about knowing that the hull is structurally sound. Few thoughts to consider.
Best of luck to you. Any questions, just ask.
I am also notifying our resident expert on fiberglass/gelcoat
ondarvr to chime in. If he says anything different than what I mentioned follow his advice. He probably forgot about resins, fiberglass and gelcoat more than I will ever learn