Adding a winch eye

I think you are talking about a trailering winch eye but not sure.
Please expand or define winch eye. Where do you want to install it?

If you know where you want the U shaped eye bolt. You need to get to the back of it. I have done upgrades where the U bolt has near and pulled out of the hull.
I use a heavy gauge pipe and float it in with high density epoxy. Float the 2 foot pipe rite in the stems V. The epoxy will be thicker than cold peanut butter.
2 plus days later, drill in your U bolt holes. Do not skimp on the threaded length , diameter or cost of the U bolt.
Seal it in with 4200 and go.

Our work boats needed a strong point to pull backwards on. I used to set 2 U bolts in the stems, this way and it pulled hard well.
One at water line with a 20' x 1" hawser spliced around the U bolt with a heavy thimble.
Another reachable for a second line if needed.
Deck cleats were never strong enough & exposed to the crew/operator/customer (not safe) if anything came loose on either end.

If you are going to try and winch that fat Carver up on a trailer, Do above with a fresh dual ( no cheap **** here either ) compound rig and stand back.
If you are not competent to prep and drag a hulk up a trailer, please consult a pro. People have lost body parts and more, trying to move heavy objects.
Your needed equipment will not come from Harbor Fright as a hint.