I think the only midarm machine you could purchase for under $1,000 would be a used stretched machine (stretched Juki or stretched Singer), and they would not be the high-speed stitchers. I have a Voyager 17 which is a stretched industrial Singer so it has the higher stitching speed; however, it would be hard to find one of those used for under $1,000. If I had to choose a machine in the under 1K price range, it would be the Juki 2010Q. However, that is a shortarm machine; to be considered a midarm, the machine needs to have a harp size of 13 inches or larger.
Your best bet would probably be to keep a close eye on craigslist; some people get lucky that way.