I have used Calgon and only calgon for years, even with our Class A. Works great and we have never had any smell. Chemical or otherwise!
When you use Calgon, rinsing is easy because it breaks down everything.
After dumping, when getting ready to leave a campsite, I pour about 2 gallons of water and 1/2 cup of Calgon for the trip, home or the next destination.
I have a friend that uses the rid-ex method, and swears by it. They spend about 6 months a year mostly
dry camping. So for them this works well.
Of course before winter storage a good rinse or two helps to prepare for non-use.