[travelin texans]

I had 2 greys & 1 black. One grey was the galley with the dishwasher & would last a couple weeks before dumping. The other grey was the lavatory, shower & washing machine & I left it open when connected or I would have been draining almost daily, I closed it a day or 2 prior to dumping the black for rinsing out the hose. I did however always leave a sag in the drain hose which acted as a P trap to prevent park from venting back into my rv, worked great. Ten plus years of fulltiming doing it this way & never had an odor issue.
You have 3 greys so I'd suggest to only open the one that fills the fastest, probably the shower & put a sag in the drain hose.