I think I’ve resolved it, or at least much improved it. There are four main components to my solar charger: the solar panel, the battery manager, the battery itself, and the USB output (the mintyboost). The panel is obviously fine. I’d been worried the battery was damaged and I haven’t quite disproven that yet, though I doubt it now. But it may have been a soldering issue on one of the other two.
The mintyboost is an all-solder situation. You buy the kit, it comes in a package and you get to assemble it. I believe I’d done fine on that, though hearing that another individual had had troubles with theirs, I cleaned up all the solder joints and redid a couple for solid connections.
The battery manager, though, needed just one soldering change. I had to take off one resistor and replace it with a lower-ohm resistor. That part wasn’t difficult, but on further examination it looked like one end of that connection wasn’t as solid as it should have been. I fixed that as well.
So with the problem going on, I had been getting around 300mAh out of the battery after about two days in the sun (which the solar panel is supposed to do in an hour). I just tossed it outside for maybe half an hour and got 90mAh out of it. Significant improvement, though I’ll have to keep playing with it.