Easy standpipe

In my basement I have an old cast iron sink that is properly drained and vented to cast iron pipe.

I will be replacing this rusty old sink with a new utility sink. No problems there.

Currently, my washing machine drains into the sink, and one possibility is to continue draining it into the new sink.

But I am thinking about possible ways to make the set-up look neater.

I would like to install a standpipe. I understand that I would need to vent this. I have seen Terry's diagram about how I could do this and vent it. However, I do not really want to do it this way, given that I have iron pipe. Rather than go to that trouble I would opt to continue draining into the sink.

But I have also just read about Air Admittance Valves.

So here is my question.

If I plumbed in a stand pipe, with a p-trap and an AAV and then joined this to before the P-trap on the utility sink (which is normally vented) would this be OK?

It may not work...AAV's allow air in, not out (unless they're broken). A washing machine pushes a lot of water out, creating a big air pressure wave. A normal vent would allow that to equalize, an AAV wouldn't. Just my 2-cents...