[Silhouette]

The most success I have had with per project pricing is having a discovery phase to actually scope out the work.

I concur. Also, the discovery phase itself can be flexible on time allotted and billed in time increments, even if the main project won't be. You might well not know up-front whether you need a day, a week or a month to pin down the spec and all the other details, so a self-contained "getting to know you" phase before anyone makes big commitments has a lot of upsides for all parties.

Also, regarding the problem of vague requirements and differing interpretations, getting a complete set of acceptance tests agreed early-on has a lot of upsides for both parties too.