Hi Joe-

Hellmanex should work well, especially if you can get some agitation while rinsing. The only way to find out is to test it. The concern, of course, is that the dye may bind tightly to the plastic, requiring rubbing to remove it.

Fluorescein forms very soluble salts with bicarbonates (like sodium bicarbonate) or dissolves in organic solvents like acetone and methanol (not ethanol). If you want to use it, wash it off your glassware prior to using washer. I'm not sure about Hellmanex, it's phosphate-based, so it's basic, but might not be sufficent.

Yes, Hellmanex will clean it off. Rinse with water afterwards.