I have recently wired my Honda 350 (temporarily, ignition and charging only). I am using an aftermarket, solid state regulator/rectifier unit which I purchased more than an year ago from Oregon Motorcycle Parts. The proprietor, Tony, is awesome. He builds these himself or sells a few selected universal ones that he trusts. He answers all your email questions.
Because my cb350 uses a fixed magnet alternator, I should in theory be able to run without a battery. I tried this yesterday and it works like a charm. Instead of the battery, I installed a large 4700uF capacitor. Starts right up and runs great. I ran it first with a battery and then swapped out the battery for the capacitor. The engine was warm, so that may account for the easy starting. I have yet to try it cold.
Tony at Oregon Motorcycle Parts says he is working on a prototype of a battery eliminator (capacitor) which will be rated at 15,000 uF which is supposedly much better. I have told him I am happy to try one on my bike if he needs a guinea pig.
There are also some other battery eliminators on ebay. Most are like mine; small cylinder shape about the size of a D cell battery. I have emailed the vendor of the rectangular one for the uF rating, but he never got back to me. I guess I won't be buying from that guy.