Is there anything in New Hampshire that is preventing you from being this kind of contractor. Where I live, and that would be Illinois, I am a 1099 contractor for a couple of outfits that pay me as an independent contractor. There is no problem here.
I would think that as long as the firm that hires you files the 1099 form, that there should be no problem with it being "official." However, I don't know the laws that apply to that sort of thing in New Hampshire. Maybe there is a difference there as compared to where I am.
I did find some information on the following site which you also might find to be helpful.
What is a 1099 Contractor?