Bsmnt Laundry Proposed Drainage

[ScottDee]

Since it's COVID season and I'm home bound, I'm dreaming of how to move my laundry to the basement. I did up a sketch and I'm wondering if anyone can confirm that this is a reasonable way to put the drainage in for a laundry tray and washer standpipe. The existing drainage is a bit wonky, so I'm hoping to just tap into the stack, as low as I can, and reuse the venting from the old laundry room on the floor above. Advice / criticism would be welcome!