So it ends up two of the four batteries I got are dead. Thankfully, I have plenty of enloop batteries around to test. I wired up three to get my 3.6v (4.2v technically, but that will drop as they discharge), and the radio seems to work just fine. I do need to devise a better holder system for the batteries, as taping them together has been flaky at best.
I hope next week to have something better in place for the batteries so I can test the charging of them via the radio. I should also have done a little bit better testing of the solar cell so I can see what kind of voltage I need with the new cell (I'm guessing ~4.5v- 5v.)