Oh I'm sure a few of us here have messed with the Green Ringer.
I've owned three: one built by JD Sleep (GGG), one built by Death By Audio, and one I built myself.
The ggg one had a lovely smooth ringing sound; the dba one was more of a dissonant distortion like you describe; and the one I made was somewhere in the middle.
I tried several mods for better low end, with no success. The dba one had a clean blend, but it phase-cancelled out the lows.
So the ideal IMO would be to tweak the ringing effect for smoother tone, and then use/incorporate a blender that has either a phase switch or a crossover.