Let's see if I understand this query.
--- You have a wiring harness that no one knows about but you. Meaning: it is impossible for us to check your wiring connections.
--- You have a reg/rect. that wasn't made or offered by Honda, and we have no specification or wire pinout/connection data for it, or any reference numbers to locate this info.
--- And your question is "what should you check"?
I'd have to guess the answer is: EVERYTHING !
But, I'd test the system with lead acid type battery, as they are far more tolerant (and cheaper to replace) while you get things sorted.
From the antigravity web site FAQ...
"3)Also, important is that OVER CHARGING above 14.7 v can damage Lead or Lithium batteries. For this reason older bikes should make sure their eletrical system and specifically the Voltage Regulator is operating correctly or you will find youself damaging your batteries if your bikes charging systems voltage to the battery is going above 15v."
They sure put it mildly, so as not to scare off any prospective buyers. Each time you overcharge or undercharge the Lithium batteries, it's capability is diminished.
I expect it voids their warranty, as well. But, they didn't put that fine print on the web site (that I could find).