I would recommend they keep you on for the duration of the stay and then terminate after the current booking. 

Big problem is that fraud and unethical behavior can be very profitable short term in syndicating investments.  

Note, of course, that this opinion is coming from a place of the very limited information you supplied in your original post but on the face of it living for $1500/mo in a decent neighborhood seems decent to me.That said, I would encourage you to look at this more long term. In

Lease has following clause so no early termination clause.  

Anyone who makes friction for other guests can have their lease terminated and that should be very clearly spelled out in the lease itself.

You either fix the door to self close, let it go, or terminate his tenancy.

They will typically button him up immediately.I would give the tenant two options: permit entry and showings with at least 24 hours notice, or allow them to terminate and vacate without penalty.

They have pleaded for an exception, but lying on application is clearly listed in lease as grounds for eviction/lease termination.  

If you have Bloomberg terminal and the resources to give yourself an unfair advantage, sure, go for it.

I was even thinking of when I send him the termination letter asking for those 2K back.