Hello XXXXXXXXX and welcome to just answer, Super mechanic here. I just have a question about your Caddy.
Did you try turning the engine with a socket and ratchet To make sure the engine turns?
Auto Mechanic
ASE master, 30+ years. All makes and models. Trouble shooter, shop forman, service manager
If the engine turns good, and the starter is getting hot, battery fully charged then it is either not messing right with the flywheel or the starter has a short in it.
Are you sure the connections are clean and tight?
There is one thing that can fool some of the best techs. When you look at the starter, comparing it to the original one. You want to make sure that the gears are the exact same size, with the same number of teeth. Also, the angle of the starter "nose" may look the same but there are some with a slightly different angle where the gear is.
It's kinds hard to put a starter in wrong, there must be something with the actual functioning of the starter.