Does a group like this even exist?

The left has ADA (Americans for Democratic Action), the right has the ACU (American Conservative Union) both of which spotlight and reward legislators who stick most frequently with the “party line”. Is there a group out there (hypothetically called Americans for Principled Action or something like that) that spotlight and rewards legislators who most frequently break with their respective party lines?

No Labels might be what you’re looking for

Unite America

If it did there isn’t anybody they could support.