Here is another perspective.
You have changed you stator because your old one failed, we can assume? And we should assume that you are reading stator voltage at the battery terminals? I think (it has been awhile since I have had one) the the assimilator fails in the closed position (light on)?
That being said, your battery has been stressed and has more than likely lost some, if not all, of its internal memory. This is now a weak link in your system. By what i have read so far, this battery is failing. Even if only one or to seasons old, it does not matter.
You can charge it with a trickle charger but this is not what it needs. You need a good charger to, hopefully, bring this back to life. Then, take it to the auto parts store and have it tested. Just putting it back in the bike and turning on the light is NOT all well and good, and will leave you with questions and perhaps stranded somewhere, where as a tool meant for this will leave you with definite answers.
Many of us profess to now all about batteries but there is one universal truth, a weak battery is soon to be dead, new stator or not.
Bottom line!
My advice is to bite a bullet and match that nice new charging system with a nice new battery and ride with confidence into the night.