The wash times are very short for RC paper.
I wash mine by having two trays stacked one above the other. The water flows into the top tray, and then flows out through some holes I've drilled near the rim on one edge. The outflow falls into the bottom tray.
All my prints go from the fixer to my bottom wash tray. They get a fair amount of flow and agitation from the falling water. They stay there until an opportunity arises to move a single print up to the top tray where it is washed individually for at least one minute, but no more than three minutes, in the flowing water. I then take it out and move it to the drying area.
When I'm being efficient, I can do the final stage of washing at the same time as agitating a later print in the fixer, all the while waiting to turn on the light to examine the later print.
You could probably use the item you linked to instead of drilling holes in the top tray.