Yes address the source! Smart move. Consistent water changes with zero TDS RO/DI water, running good mechanical filtration like CPE and Purigen, aggressive skimming will all help. Another thing is to increase flow in the area of the red slime.
One good idea is to use the turkey baster right before you do a water change, get the red slime up and in the water column and then siphon it out for a water change.