J-cloth to the rescue
My plywood/fibreglass sink (now over 24 years since I built it - ouch, the reality of middle age bites you when you think of things like that) has the aforementioned non- recessed drain flange. I acually like it. The washer usually sits in, or drains into the sink, from a shelf beside the sink. The small amount of water that lays in the sink is under the slatted duckboards that I use to put my trays at a comfortable height. Any splashes from the trays land on a wet surface. At the end of a session I flip the duck boards over so evereything gets wet, then wipe the sink down.
This keeps the chemicals that we dissolved to make up developer and fix from re-forming once the spill dries out. Dried chemiostry floating around as dust will drive you nuts in spotting until you get it under control.
Wipe down is carried out with j-cloths salvaged from the kitchen sink when they are deemed too far gone to wash dishes with. The once wet are a great wick, when you lay one over the open drain.