Thanks, everyone, for chiming in and helping me with this. I have some good news and a bit of a somewhat anti-climactic solution to my problem.
The good news is that the charger is working again! 🙌🏽
On the less satisfying side, the problem fixed itself when I adjusted the power cables connected to the power supply. The lugs holes on the wires I used might simply be too big for a good contact. After adjusting them and clamping them down a second time, the power supply magically worked.
I did clean up a couple of other things while debugging this. Even though I saw the RSP-750 charge my batteries once, I did have a wiring issue with my current control wiring. Per Dacian's suggestion (sorry, I accidentally private messaged him), pin 7 goes to my device's voltage source and pin 11 goes to my device's ground. I'm using an Arduino to send 2V so that it lowers the charge current for the time being since my battery pack isn't very big. Once I add more batteries I will adjust the voltage accordingly. Thank you, Dacian!
I still don't fully understand the role wire thickness plays here. One of the suggestions is that my wire thickness + short length may play a role in preventing the charger from kicking on. I am having trouble conceptualizing why. That said, I will replace my 6AWG wires with 8 AWG wires that I have lying around and in the process make sure the lug connector has a better fitting hole. Sounds like 10 AWG is even better in this case, but I don't have any handy.
Thank you again, everyone for the help; I'm learning quite a bit in this process.
-Roberto.