Then you are trying to solve this problem with one of the most effective and simple solutions available. No matter how complex the logic you build to prevent/automatically delete unwanted spam posts you are essentially GUARANTEED to a) miss some fraction of unwanted posts and b) delete some fraction of false-positive valid posts.

I wish you all the luck with whatever approach(es) you wind up taking, but it seems to me that you are constraining yourselves to REACTING instead of being PROACTIVE. Putting a simple, easy verification in front of each new user is a TRIVIAL amount of effort for each new user to take care of while providing benefits for ALL of us, including your staff that currently have to wade through the posts each day to remove unwanted ones. It seems intuitive that such systems are effective given how many sites have moved to implement such initiatives.

UPDATE: I read the post to say "not going to stop UNWANTED people from signing up" - i.e. a better form of new-user verification than is currently being used.