Have you actually looked at visas? I think it's highly unlikely you will be moving next month, regardless of the offer.
Last year we moved to the US, however, this was after my husband working for the UK branch of the company for over a year, before being able to apply for a transfer to the US. It took 18 months from him starting with the UK company to us getting our L1 / L2 visas.
If he has exceptional skills, then he may be able to get a different class of visa, however, he would have to be published, etc in his field.
The other option is the H visa, this means that you would have no option to work, ever. However, this is done via lottery every October, and the closing date for this year has already passed.
He absolutely could not get paid self employed, he would need to be an employee of the company and they would have to sponsor his contract, unless it is a very short term assignment, in which case that may change.
I'm not wanting to piss on your parade, it is an amazing opportunity, but the visa really is a massive issue that may mean this cannot happen.
I wouldn't get advice from an international tax expert at this stage, you need to get an immigration lawyer to advise you of the options available