The root cause of all the symptoms that you are describing is that your client hasn't got the proper knowledge, experience and mentality to (co-)develop something innovative.
How exactly is "a process" going to change that so rapidly?
(I haven't a simple answer and I am also struggling with this problem..)
I think clients in this area tend to not want "innovative". From my (admittedly limited) experience, most clients want "a website". A process can help the user understand what is needed to go from nothing to a website.
It works well when the website is an aside to their goal e.g. selling watches. The website is merely a facilitator to this. By setting a process, you can gauge your client's capacity to work with you on the project. If they don't like how you do things, you can compromise or part ways, amicably.
If you are building the product that the client will sell directly (e.g. a web service) then I believe that a process alone isn't going to overcome the fundamental difficulties of the project - namely that your client is probably selling something that they don't fully understand.
How exactly is "a process" going to change that so rapidly?
(I haven't a simple answer and I am also struggling with this problem..)