Okay, leak report was legitimate, as I didn't have the drain pump properly screwed on--it was kind of on at a little angle, so all of the water was just running out of it. Again, good thing I only dumped a couple of cups in to test it, as that could have been a real mess.
I made sure it was on right this time, set it upright, and I turned the unit on and it gave me a 4E error! Again, I thought maybe this was just a remnant from the prior problem, so I ignored it and decided to hook up the water line and give it a shot.
While I may be jumping the gun, it looks like it's working--I'm currently in the "Dry" cycle and it got to it with no issues. Water draining was good and swift into the disposal.
So, to sum up, although the drain pump reads 0 Ohms across the terminals, that does not appear to be a problem. The replacement pump I got also reads 0 Ohms across the terminals and my original pump seems to be working fine now that I replaced the main board.
As far as the main board, I just noticed in my manual that printed circuit boards are supposed to be under warranty for 5 years, so I'm going to see if Samsung will send me out a replacement if I send them my damaged one. If so, I'll just hold onto it for a spare along with my spare drain pump...
Thank you for all of your help! I would have never stuck this out if it wasn't for your assistance!