Hey guys! First of all, I would like to thank you all for being so responsive and willing to help. This forum has been a tremendous resource this past week as I encountered one obstacle after another fixing various components in our hot tub.
I ended up calling Dream Maker this morning, and the person I spoke with was great. She was very knowledgeable and after some discussion she determined that the board is more than likely the culprit. Since the board was one of the new parts, purchased last fall, she RMA'd it without hesitation ($400 part, so thank goodness!). It should be arriving in 7-10 days.
In the meantime, I still had the old control board in the garage. I decided to get creative by removing (desoldering) the pump power cord molex connector and soldering it to a medium-duty extension cord (14/3) that plugs into a GCFI electrical outlet. Doing this enables me to bypass the control board and plug the pump directly into an electrical outlet. It also helped reassure me by confirming the pump is in working order (the pump is brand new, too!).
I've attached a photo of my bypass. Ignore the terrible soldering job. I am going to redo the entire thing using the second identical molex connector on the board (one for pump, one for Ozone). I made some beginner mistakes, but I'm confident I can do a much better job redoing it. Each wire I soldered (three wires) was much better than the previous. I tested the pump and ran it for about a minute, and I felt victorious in this never-ending battle with the hot tub.
Hopefully everything from here on out goes the way it's supposed to. I've learned a LOT, but I'm ready to just enjoy all of the hard work for a bit.