So, after shopping around a bit and realizing I'd be ripped off if I bought the parts for this fix as originally intended, I decided to go with a 24 hour timer with on and off pins.

Upsides are that I don't need to figure out how to keep things on for long periods of time and I can use it to schedule the charging of things if I want. Plus, if I forget to set it, it automatically turns things off. It is quite idiot-proof.

The downside is that there is going to be some parasitic load associated with turning that thing 24 hours a day. I imagine it's better than leaving the things turned on even one night a week over night, but I'd love to have a watt-meter to check it out.