I'm just going to post a few guesses here but it'd be nice if someone more skilled would weigh in.
Your stock light coil produces 6v "nominally". It's only a suggested number since, unregulated, it probably ranges from about 3vac to 18vac on a fairly straight voltage/rpm curve from idle to max rpm. That's why it's 3v dim at idle and 18v bright when top speed. You kitted it and raised peak rpm enough to push that coils top over the 20v point and the bulb finally reached it's limit.
So let's say your coil, at low rpm, is putting out 3 to 6vac. No problem so far. But if you put a 12vac regulator on it it's probably not going to kick out any voltage at all, no light, until you're at medium rpm at feed the regulator something it's at all happy with.
If you put a 6v regulator on it, it'll probably )still guessing here), kick in the lightbulb at a lower rpm, but limit it at some point below the max you've been used to, unregulated, at peak rpm.
In order not to have any of these tradeoffs, you'd have to replace the 6vac coil with a 12vac version and run the 12vac regulator. Then the coil is producing enough juice to meet the lowest demands of the regulator at idle, and light the light, as well as deliver the 12-16vac to the bulb that your new kit is delivering, but the 12v regulator will protect the bulb from the 20+ (probably waay plus) vac that your new 12vac coil is pumping out of your new screaming kit.
I have no fucking idea what I'm talking about here. I've never measured any of this. Just hunches based on quite a bit of trial and error and rudimentary background in electronics.(edited)