House has no plumbing vent — is this a solution?
I am not a plumber but I think your plan is just fine according to these tables:

http://publicecodes.cyberregs.com/icod/ipc/2012/icod_ipc_2012_7_sec009.htm

http://publicecodes.cyberregs.com/icod/ipc/2012/icod_ipc_2012_7_sec010.htm

A 3" pipe is plenty for the number of DFU's in your stack and horizontal run. The 2" vents on the sinks are probably even oversized and so they should be plenty.

The only issue I see is you can't take sink through the roof as a 1.5". At least not here in the north where it could frost over.

Have you considered tying the kitchen vent into your main vent and avoiding another roof penetration? Just a thought.

The only time plumbers around here use 4" in a single family home is for the main sewer exit from the house, and then only a few feet of the exit itself.

Good luck!