@Betwixt - I want the workout load to be about 260mA. According to the manufacturers website, the charging current of the batteries is 200mA x 16h. I would like the circuit to be able to run 10 - 14 hours a day. 12 hours would be ideal.
@BradtheRad - You say add more panels, what if I used a panel big enough to power the batteries? About the PNP transistor, I actually just reread the DIY, I'll include a quote.
"...we use a PNP transistor that is controlled by the voltage output from the solar panel. When it's sunny, the output of the panel is high, which turns off the transistor, but when it gets dark, the transistor lets current flow..."