I reviewed the questions on StackOverflow with the Project-Management tag from March 7th to April 12th, and there aren't any questions that stand-out as being something that would be on-topic here.
SO Questions with Project-Management Tag:
Many of the questions are just more of the "What type of software would you recommend" type questions that have already been answered here countless times.
Some of the questions were about building project management systems and were actually on-topic programming questions for Stack Overflow.
There was one good question that was asked again over here on PMSE. I flagged it for closure on Stackoverflow.
Suggestions from Main Meta SE:
However, that doesn't mean that this isn't a great suggestion or that showing some sort of lightbox and recommending a more targeted site isn't something we could look into. There was a similar question on the Main Meta SE site, and Jeff Atwood's response.
Jeff suggested editing the tag wiki to specify that questions using that tag might best fit elsewhere, but the community team didn't necessarily decline the feature request or this suggestion that is similar to yours.
In summary, we could first try editing the tag wiki on SO, but I'm not sure that it would inject quality questions into our site. I have edited the tag wiki there.
Finally, we must be prepared to continue to allow only high quality questions on PMSE and close ones that need improvement. In some cases, after edits, closed questions can be voted to reopen or flagged for moderator attention. Closing is not a permanent action, but it does serve as signposts that help define the site and encourage quality over quantity.