What is your experience with keyword phrases that don’t make sense but have a great KEI, an example might be something like “fax loan no payday.” Now this MUST BE something people type in SE’s because it you rearrange the words and do a Google search you’ll see that you get a vastly larger number of searches for the latter. Yet, while it may look odd as anchor text, these phrases deliver a high KEI and seem like it could be a wise choice to use these.
My guess would be these phrases aren't being searched. I've spent countless hours looking through my web logs for dozens of sites over the years and and I can't recall finding nonsensical phrases pulling in any significant traffic. However, you could always test a few of these phrases on your site and see what happens.