I should probably keep quite, because it's been a while since I worked on one, but the dreams electrical system is notoriously weak. If your running the stock rectifier, the big orange one, then, if memory serves, you should replace it with a modern one. Seems I got mine from a guy in Oregon who specializes in old honda upgrades. Sorry to be so vague.
Also, a lot of folks put in as much led's as possible to put as little drain on the system as possible. maybe you said so earlier in the thread, but have you gone to the Honda 305 forum?