One of my students last year wanted to stay in UK but ended up going home because of a visa issue. And I thought the politicians were keen to retain quality eng graduates in the country. So your visa plight is not unknown to me.
Structures jobs seem to be prevalent nowadays; if you can do structural analysis and use the software packages you're in a strong position. CFD skills come a close second, but anyone can run Fluent so competition is greater for those jobs than structures ones.
Doing another degree will just delay the inevitable.
If you want to fly, fly. Find a way to do it. Pprune is stuffed with advice about private or professional flying. But it's rare to find a position that combines both engineering and flying. There are certainly plenty of professional pilots with aero engineering degrees but who've never worked as engineers, and that's a different thing. I know perhaps half a dozen aero engineers who need their flying qualifications to function as engineers, and vice versa. Rare breed indeed.