In my opinion, the best way to advertise the site to MO-users (and I assume the same is true for math.SE users) is just to create an interesting site.
These sites' communities where repeatedly informed about this site's existence. I think people are aware of it by now. And, I think we should not do more direct broad advertizing there. I rather feel what was done so far is already at the threshold of what is considered annoying.
There might be room for some very targeted advertizing: if somebody knows of some (old) questions that got closed as off-topic there but would be on-topic here, they could leave a comment on it to point this out to OP. But, even with this I would be careful.
Let us not oversell the site. Let us work on making it better.