I've done it
It was over 10 years ago though. I was at a job fair in Wisconsin, realized that I probably wouldn't get a job in a Wisconsin or Illinois school and started talking to the Texas schools that were there.
The attitude was more of "Wow! You're certified! Please come work for us." I got my first job there.
Before that I was contacting state education boards and finding out what the requirements were to be certified and trying to find job postings in different states. It was before the internet exploded, so things were a little harder then.
I'd pick a state or states, contact the education boards to find out about certification, and try to locate job posting sites. If you find a city you're somewhat interested in, start looking at the websites for those districts in that area. Here in Texas we're broken up into Regions. At one point we could file an on-line application in the region and districts would download it. That's how I got my 2nd job.
I'm not sure it this helped at all, but it is possible to get jobs in other states. I'm not sure where you want to go. Obviously states with teacher shortages make it easier than states that have more than enough teachers. They might actually recruit at job fairs.
Good luck!