Some thoughts:
You said you started at 1/3rd full. The way the sensors work, you might have been just shy of 1/2 tank. Best to start with empty holding tanks, except for a couple gallons in the black tank to avoid the "pyramid".
I'm puzzled by the gray backing up in the sink. It should have backed up in the shower?
For us, the showers can eat up the water. Wet yourself down, turn off the water, lightly suds up and a quick rinse.
Washing dishes- use disposable plates/ cups etc. it's easier to dump trash than waste water.
If you hook up at an electric/water and no drain site, you can use a lot of water very quickly, filling your gray tank. When using those sites, we stay on the onboard fresh water tank. It should run empty before the gray overflows.
Norm
