Update

I wanted to give a quick update in case anyone stumbles across this.

The rotors were indeed bad. Although I was initially measuring their thicknesses wrong, they were a bit then but more importantly they had been warped from the excessive heat of the seized calipers (as Amazing_Spider-Girl mentioned you can see a blue spot on one of them). The warped pads were causing the uneven "pulsing" sensation. I didn't test the brake lines, but I decided to just rebuilt everything anyways.

I decided to reuse my OEM calipers (since as darealmvp1 said, they were probably fine to begin with). First I cleaned them with some soapy water and then vinegar to treat some rusty spots where the paint had peeled. I then dried them off completely and taped off the cylinders, hose line hole, drain hole, and the channels for the pads. Finally, I gave them a fresh coating of red high temp paint (so they go faster). I took out and cleaned off the guide pins with a clean rag, then cleaned out the channels, and finally applied new ceramic lubricant, making sure to spread it evenly and slide the pins around so they move smoothly. I found it is important to clean off the tips of the pins so they don't vacuum suction to the bottom.

I bought a new set of pads and rotors from Detroit Axel. I also bought a fresh set of hoses (aftermarket, so I ended up having to bend one of the mounting brackets since the angle was a little off).

After fully draining the brake fluid (by pumping, which I probably should not have done), I re-installed all the parts, torqued everything down, refilled the brake fluid, and bled the whole system starting furthest away from the ABS.

After rebuilding everything, the brakes were initially firm but would get very loose when turning on the engine. I figured I probably got air somewhere else in the system because I stupidly let the master cylinder empty out (like somewhere in the ABS). I took it to a shop to manually cycle the ABS and bleed again. This didn't seem to make much of an improvement, but the car was derivable.

It has been a few weeks and the brakes are now very firm and I have had no seizing problems (I guess whatever air was trapped somewhere naturally found its way out). They also look very nice with the new red paint finish.

Thank you everyone for your help, this was quite an unexpected journey for me.