Well I jumped around from website to website.
One you may find interesting is Schistocerca Information Site
I couldn't find any info on if they can breed continually throughout the year.
Although I did find a species of band-winged grasshopper that I believe would be able to breed continuously. It's called the pallid-winged grasshopper.
I'm just going to try many different species next summer. There's quite a few in the u.s. that seem to be good candidates.