There's a number of problems facing you at the moment.
First, an awful lot of US citizen instructors are looking for work so schools are bound to be more selective in who they hire.
An M-1 visa CAN allow you to gain some post qualification work experience, currently 1 month work for each 4 months of completed study. If you do all your instructor ratings in say two months (which is realistic) then you wouldn't have accrued enough study time to gain even a 1 month work credit. The M-1 visa and related work opportunities is better suited to those starting from scratch.
The final alternative is for the school to petition immigration for a green card, usually the H visa program but again, with so many local instructors available it's a long shot.
You could of course get married (!) but realistically speaking I'm sure you can use your FAA instructor licenses in the UK, doing BFR's, IPC's and maybe even some training on N reg aircraft.