Your lack of a grey water tank drain system was built for a campsite where you can remove the cap and water the bushes with wash water. We no longer to this and it is no longer allowed almost everywhere.
If you leave your drain cap in place and open the black tank valve, you can indeed put gray water in the black tank. When you shut the valve and take the cap off, you have a mess to deal with. Not recommended.
You can purchase a 3" Valterra blade valve mounted to a bayonet fitting that will attach to your sewer outlet as well a provide a fitting to connect your sewer hose. Then shut this second valve and open the black tank valve and fill the tank. When it is time to empty the tanks, connect the sewer hose and open the new Valterra valve and drain the tank as usual.
Maybe your best bet is to purchase a portable waste water tank and drain grey water into that. Then transport it to the dump station. Many folks do this.
WBCCI #8607 VAC Region 11
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