Does anyone see a problem with stacking single sanitary tees on the vent stack to attached the toilet and bath tub?
I do! You may not discharge a major fixture, such as a toilet, past a unvented minor one, such as your bathtub. A typical bathroom installation goes down like this. The lavatory to connect to the toilet drain line and vent to the roof or revent back in the attic to a existing roof vent. The tub to connect to the lavatory drain line and be wet vented by it as will the toilet. Be advised to always check local codes before changing or remodeling your drainage system.
Second issue. The newly installed laundry/washing machine is approx 6 feet from the vent stack. I can not find the code, but believe this horizontal distance is too long for a washing machine.
For a 2" drain the distance is 5 feet from trap to vent. Most inspectors will let you fudge a bit if it's close. Good luck and thank you for rating my answer. Tom