That filter is a great idea for injecting the chlorine into the tanks, you could refill the filter a few times to get the required amount. The Roadtrek manual states 3 hours so I can't say to do it for less time. I think I will buy one so I can use it to dose the tank each time I fill.
I would at least use some of the Camco water treatment when filling the tank. When we are travelling we always sample the water to see if it is loaded with iron before taking on any water.