Thanks for the suggestions. Things are, well, still up in the air, and a bit more interesting...
Position A: I wind up signing the updated SoW due to the way things have worked with B (more on that). The day after signing it, the consulting agency I am sub-contracting for tells me that it is part time with possible of full time and that I shouldn't leave my existing contract (this goes against everything I was told at the beginning - led to believe I'd need 50%-70% on site at the beginning, has turned into 100% on site just only part time). Turns out this is actually a 10-12 week part time contract that will most likely be extended after this period. They are expecting 20 hours be billed and while they can approve more, they will run out of funding for the contract (though getting more will not be an issue given importance of project).
Position B: The head of HR and I talked on Tuesday. The background check still had not cleared (going on a week+) and he asked if I was required to give 2 weeks. I said I am not technically required to, but I would not feel right given less.
I am still working the main contract I have, but my goal was to get out of that contract soon. The work just isn't there for a full time cycle either right now and the rate is too low and I have no plan on renewing the contract given the type of work. The rate for A is too low and it is part time, but if the contract is extended then I could theoretically justify asking for much more (I'm sure the offered amount is lower).
My fear is that B is looking into someone else that is capable of starting sooner. I know the hiring manager wanted me, but given some of the statements, I'm wondering if that position will be pulled out. Granted if it is pulled out because either (a) I didn't provide the income verification they wanted or (b) wasn't willing to screw my existing client, then I won't feel too bad about it.
I was hoping to use A to get out of my existing client. I can't afford to be on site 20 hours a week with A and work my existing client. The time just isn't there and the rate is no where near enough to support full time (they would need to double it).