So after much prodding from many of you on here, I decided to order a small battery for my bike.
http://www.ebay.com/itm/271655920532
What sold me on it was information from some users who mentioned that they had ignition issues and trouble tuning the engine which was often misappropriated to the carburetor. When I did run the engine to get the timing set, I was having some issues with poor idle and the carb seemed to be jetted too lean. I'm wondering now if this wasn't an electrical issue the whole time.
I did some additional research and still have a few questions. I'm wondering why a battery performs better in this situation. Assuming both a battery and a capacitor are charged to the same voltage, in theory a battery would provide consistent voltage across it's lifespan until the point where it reaches the end of it's life and begins to lose charge rapidly. In a graph of voltage vs. time, this would be a horizontal line with a quick drop at the end. A capacitor would look more like a steadily descending line, losing voltage throughout it's lifespan until it is no longer functioning.
In a charging system however, like on our motorcycles, the PMA is sending energy through the regulator and back into the battery or capacitor. If the issue with the capacitor's performance for our application is due to the decreasing voltage during use, wouldn't the charging system be feeding the same amount of voltage that it's using? Or is that why people are having trouble closer to idle...maybe the voltage being supplied during idle is a net negative and this causes the dimming of the lights people describe. So that's a potential downside for the capacitor.
On the flip side, some have mentioned that using a small battery with a PMA can be dangerous because it can actually overcharge. I'm not sure why this would happen with a regulator in place, but I'm certainly no expert on this and am curious to know. If I run this battery I linked, I would hope that it would be more suited for long trips, as opposed to dangerous but just in a different way.
There is then the option of running the two in tandem, but I'm not sure what benefit this provides. Feel free to chime in if you've got any suggestions or if there's something I'm missing.