The real solution is to fix the problem with the gray tank vent. You need to get a vent from the gray tank, high enough to be above the fluid, out through the roof.
I can see a couple of ways.
1. Drill another hole in the top of the gray tank and install another vent line making sure the bottom is high enough. Put an elbow in it and "T" into the current vent line so it goes through the roof.
2. Cut the existing vent line BELOW where its "T" goes to the sink. Pull the vent out of the tank and cut it off so it only sticks a couple of inches into the tank. Re-insert it into the tank and use a coupling to tie back to the remaining vent line.
Do it right, and you do it once. Be sure that you get a good seal around the vent where it enters the gray tank with either of these two repairs.
Anything else still leaves you with a pressurized tank when it starts filling. If you have a pressurized tank, you WILL have problems no matter how you try to patch it.