If the depredation products are gone then it does not matter if a little dye remains. The other way is to expose it to extreme uv to break it down.
You are correct. Regarding your second point,I am exposing this dye to as extreme an UV fluence as is possible each time I light the lamps. Only the quartz and the solvent itself blocks anything.

Or try using ion exchange resin on the now cleaner solution.
Will this have any effect on un-ionized organic molecules?

sounds like a small still in the backyard out of the house is the best way to do it.
That's kind of where I got to as there are no consumables and little doubt as to the purity.