David,
Interesting question. I have no idea whether the regionals are taking the H1B1 but I see it's for one year plus possible extensions. It takes probably a couple of months to get through school and on the line which takes a chunk out of that one year. I have no idea how renewable the H1B1 is...or what that renewal history is.
It's worth contacting EVERY regional's HR people and asking. It may be they've just not heard of the H1B1 so point them at it. It took them a long time to publicly admit to taking the E3s.
Here's the scoop for other ppruners:
https://www.migrationexpert.com/work...ade_visa_h1b1/