Why isn't there a website where a student or hobbyist group can register their balloons before they launch? So the FAA knows what balloons are in the air at any given time. I'd bet they're already tracking the governments weather balloons right now.
Right now it would be a fools errand to launch a balloon and actually expect it wouldn't be shot down.
If your payload is above a certain weight limit or density you have to inform the FAA under part 101.7. You can obviously opt to inform them even if you are under those limits. (There are some safety equipment you have to design into your unmanned balloon if it falls under part 101.7, such as a radar retro reflector and redundant flight termination system.)
Right now it would be a fools errand to launch a balloon and actually expect it wouldn't be shot down.