I don't think your short is in the carb solenoid because I don't think the tractor would run if it is shorted or failed. You need to use a multi-meter like Ironman posted. Set the meter to Ohms(resistance) and attach one lead to the black wire leaving the fuse holder and the other to ground. Try that and report back.

A question that should have been asked from the get-go, and that is...
What is the part number of the new ignition switch that you installed??
Just asking because many ignition switches look alike on the outside but make different connections inside when you turn the key.
Don't want to chase the wrong tail here.

Second question....
What is the number on the new diode you installed?? (something like 1Nxxx)

So the ignition switch HDK-152 and diode is 1N5400. I can get the tractor to run now but only if the red wire to the voltage regulator is not attached. Once I plug that wire in, the fuse blows.

925-3163 is the correct switch, not sure what a hdk 152, is it a cross to the cub cadet one?.

HD Switch Ignition Key Switch for Cub Cadet MTD White Outdoor 925-3163 725-3163 925-3163A 725-3163A 725-3163P - Dual Dust Protection System - w/ 2 Keys & Free Carabiner https://a.co/d/gH1cFUd

Your problem started with the deck lift, the main wire harness runs along the frame on the left side and runs up through the steering column area where there is a junction connection. Check that area for a wire that has rubbed up against the frame or the steering wheel shaft.

That was the first thing I did, could not find any rubs or pinches.

I'm not entirely familiar with the specific wiring on this CC but to me red means hot and black means ground so when I see a red wire plugged into a black wire it makes me wonder if that's the way it's supposed to be?

That wire goes to the carburetor solenoid, black sleeving maybe..

It's entirely possible that you have a bad voltage regulator. I don't like the B&S regulators, I replace them with Kohler VR's. This is the Kohler part # that I use 41-403-10-S regulator.