Not UPC (all I know).
A few non grey water tips first.
You only need a 3" drain for any home with up to three WCs.
1.5" vents only needed for everything but a WC.
Kitchen must have 2" drain and a cleanout...1.5" vent is fine as before.
The total vent area must equal the largest required building drain...so, total vent area is either 2- 2" vents plus an 1.5" or all into a 3" stack...but what you drew would still work, just not meet UPC.
No tee's on back for drain from WM, use combo.
I'll send a photo of UPC req'd graywater system.