Washing RC paper is similar to washing film, in that the substrate is relatively impervious to the chemistry.
I don't know that agitation has as much effect as dilution. Given the relatively small volumes used in the roller tubes, I doubt one gets enough dilution unless one changes the water in the tubes frequently.
I wash my RC prints in the following way:
1) I have two trays and a stand that allows me to stack one tray above the other. They sit in the sink or tub, with the faucet above them;
2) The top tray has a couple of holes drilled in the sidewall near one corner, which permit water to flow out at that point and fall into the tray below;
3) I turn on the faucet and fill the trays. Then I adjust the flow rate to about 400 ml per minute - equivalent to the amount required to replace the contents of each tray once every 5 minutes;
4) I put the print first into the lower tray and leave it to wash for 1 minute. I try to flip it over at least once;
5) I then transfer the print into the upper tray for one further minute, after which I remove the now fully washed RC print.
Once you transfer the print into the top tray, you can put a new print into the lower tray.
The resulting use of water is quite low. The keys to this are:
a) the water flow is quite low; and
b) the time is quite short.
The top wash tray (with the holes drilled in it) isn't an expensive darkroom photographic tray. Depending on the size, it is either a thrift store find, a discount houseware clearance item, or a kitty litter pan
.
Hope this helps