Can you get a big pump / filter doohick ?

Green gunge sounds like algae (which are quite big) so, rather than poison everything you could just scoop em out using a filter. The reason I say this is that tipping chlorine, EDTA or azide or cyanide or something will risk poisoning the rest of your garden (remember there is a difference in the concentration required to stop things goring (a biostatic) and that required to kill stuff that is already growing !).

Equivalently you could tip in a gallon of industrial herbicide and be very careful not to spill any during the subsequent 3 water changes needed to get rid of it !!

I'd go for the filter !