1) At this time, the company is financially not willing to commit to the total cost of the sponsorship. The owner has offered up the idea of creating an LLC in the US, hiring me here and then having me work "consult" there with a "stipend" Is this plausible?
Dunno. I would assume that it'd be okay for you to work for a UK company from the US, but actually coming over here to work as a consultant might mean that you'd need a work permit. Still, not sure about that.
2) Based on the fact that I have an offer, if I apply for an HSMP, how quickly could I actually expedite the approval process. If I say the start date is two months from the submission date - will that help expedite it? I wouldn't want to wait more than two months.
If you have a specific job offer, it sounds like it'd be more appropriate for you to apply for a work permit. The HSMP visa is difficult to get unless you truly are highly skilled (or deemed to be by the Home Office). A work permit, while difficult to obtain, is much easier to obtain if you have gotten to the point of being offered a job by a UK company.
As far as I know, there's no way to expedite any type of visa application. They might look at your start date, but I doubt that would encourage them to speed things along. It's my sense that most visa processes (other than spouse or fiance/e') take several months.
3) Is it possible to go over for 6 months and get paid a stipend as if I'm in training to open an NY office. Would that require any special work permits?
Well, would you actually be training to open a NY office, or would that just be a way to get you here for 6 months? And what would you do after those 6 months?
4) What do people do who go over and find jobs in bars?
People don't just come over and find jobs in bars. It's illegal to look for work (or volunteer) whilst here as a visitor. It's easier for members of the EU, because they pretty much come and go as they please. As a US citizen, though, you'll need a work permit or settlement-linked visa if you're going to work here in any capacity.
It might be best to wait until the company in question can afford to pay for your visa sponsorship. It is an expensive process, and if you have to pay part of that, coupled with a lower salary and a higher cost of living, it might just not be worth it in the long run.