I don't know of any that are particularly inexpensive (I guess it depends on your definition of that). I love my Moving Comfort Fiona. They are $44 though. Target has a high impact one but I couldn't get it fastened because of the way it is designed....you have to put it over your head then fasten part of it behind your back and I couldn't get it to save my life. LOL
They do exist - Moving Comfort and Enell both make several that really do work. I am a DD cup and my Moving Comfort one works great, even for running. They are more expensive though, than a regular sports bra.
They don't exist. Best bet is to wear an old/comfortable regular bra with a sports bra a size too small over top.
This is pretty much what I do. Sometimes I'll wear two sports bras. I know a girl who wears three... :/ Seriously though, I've only had one instance in years of running while wearing two bras where I had an embarrassing "popping out" situation! (Thankfully not a nipplegate though! haha)