You have a State Department/finance issue, not a medical/nursing training issue....cutting to the chase....talk to your local US embassy/consulate about the immigration stuff....an H1B from a hospital to train for anesthesia services would be a very unusual circumstance and one not to base decision making on. Anesthesia schools could not care less where you get the money, so long as they get paid. Research hospitals near the US/Canadian border and call the OR front desk and ask for anesthesia. Odds are you'll be able to talk to someone that might have been in your shoes. Be upfront and honest and humble and you may find what you're looking for. I'd focus moving west from the mid-west US. Start in Idaho.