One of the problems I have with CycleX is that they have woefully incomplete specifications for nearly all of their product offerings.
In the case of their alternators, they only give a maximum specification. Whereas ALL alternators have inherent spec behavior regarding power output over a range of RPMs.
Could be they have these specs, but don't publish them. But, I suspect they simply don't know the full capability of the units they sell. They only know what "works" when using the full compliment of products they sell.
We can't tell you if a bigger capacitor will help, because we do not have the power output curve of the cycleX alternator(s).
We only know that it will put out zero Amps at Zero RPM and 16 amps at some unspecified RPM. Who knows what the alternator will put out at kick start RPM? Such limited published data is woefully inadequate to make any sort of predictive circuit design modification different from the exact configuration of components cycleX offers.
Once you start buying their components, you are a junkie addicted to whatever they tell you to buy from them, and can only hope they got the engineering correct enough to meet your needs.
The SOHC4 was designed to operate with a battery. If you want to change that design successfully or reliably, you need to be as smart and knowledgeable as the Honda engineers, or be totally reliant on promises from a third party with unknown credentials, besides a price in a catalog.