Thank you so much for your help, everyone. I really appreciate the time you took to help me with this.

In the end, I remembered that one of my friends is essentially a contractor (unlicensed, but he knows much of this stuff). He's not an electrician, but he knows the basics, and he's the best "free*" option I have for getting eyes-on with the problem.

*free as in beer...beer I will buy for him the next time we're out

He checked the diagrams before coming over, and once he saw my wiring in person he had definite ideas of what to do.

In the end, we figured out which socket needed to be the primary switch. We then fished the neutral wire bundle out from the back of the box, giving us connections for five wires in total, so the primary switch was easy. For the secondary switch, we took the two black wires in the second box and tied them together, and left the neutral tucked in the back of the box. This ended up working perfectly. After a couple trial and errors on two of the switches (figuring out where the primary needed to go), we had the whole thing wired up in about 30 minutes total.

Thanks again for the assistance, guys. I did end up absorbing all your advice and using it to solve the situation along with my friend. I think the instructions with the switch could be clearer and account for more wiring configurations, but also the wires in my walls aren't very well labeled, so that hurt as well.