I don't know how you plan on replacing the transom, but I'll offer up how I replaced a wooden transom with success. I too cut the boat off due to rot and shortened it, but in doing so, I had to relocate the seat and oar locks in order to get the bow to rise the right distance out of the water.

After cutting the boat, I took a sheet of marine grade plywood and held it against the new stern and traced with a pencil around the inside of the boat. That gave me the pattern for the inside piece. Be sure to cut on the outside of the traced line (you want to be able to see the line when you are done cutting).

Then with another piece of plywood I traced the outer edge around the transom and cut that out (cutting ON the line this time).

Now I had a piece to fit the inside and the outside of the stern. Some good quality waterproof glue and brass screws to clamp things together and the new transom was ready for finishing.

I admire your sense of adventure. It has been my experience that the type of project you have undertaken always ends up costing much more than I originally imagined, but the learning process was fun and informative.

Have fun.