Wow I applaud your thoroughness in presenting your question and details surround it. If you do what you propose, you will be "wet venting" the washer standpipe and the wash basin. Every time someone flushes a toilet upstairs, you risk siphoning the traps down below. And besides, it is usually code to not have anything downstream of a toilet. Of course you'll have to check your local codes for venting requirements as well as allowable fixture units for a 3" stack, but I would have to say that the job is not as quick and easy as you think it is.
I hope you replace that washtub with something nicer...that thing is a beast!