Riaz:
I can't answer this PMBOK-ily, but I will answer it from a business owner perspective:
A,B and C are the reasons why the PM cannot negotiate a contract with a vendor. Because of the vague SOW, vendors will view cost-plus contacts as too risky because they do not know what they are getting themselves into. The only way a vendor will bite will be time and materials.
The PM may be able to negotiate the cost of the "time" aspect: The vendor may be open to reducing the hourly rate for a guaranteed number of hours and the like.
Just because the PM wants to have some degree of control does not imply that they will get what they want. I think the key aspect of the question is, "The PM is finding it hard to negotiate." No vendor is biting.
Hope that helps. If a more savvy moderator has a better answer, please chime in!
Harry