Laugh not. I've been there. Not a H1B but a work visa in another country. PhD yes, worse, lapsed but threw it around, better, business setting.
My 'way out' was to stay on and keep building good terms with his boss's equivalent in another part of the company, one of the owners. Worked out ok. Had she not been there, I'd have left.
I also worked overseas on a visa tied to my employer. I managed to move job to stay in the country; otherwise I'd have had issues too. But I didn't think it was an awful situation exactly - it was the exact one I'd chosen.
My 'way out' was to stay on and keep building good terms with his boss's equivalent in another part of the company, one of the owners. Worked out ok. Had she not been there, I'd have left.