Can you find any legal cites that refer to and debate prior restraint other than first ammendment? I understand the concept and your intent in this discussion, but I'm not sure you're putting up a valid legal argument, at least in terms of published law review.
Look at where the actual restrictions on other rights are.
You're exactly right. So, we go back and get rid of that - no background checks. How would Bob Cheek know that the man or woman on the other side of the counter is a convicted felon?
Why is it Bob Cheek's repsonsibility to enforce such restrictions any more than it is John Buck's (As opposed to "Doe's") responsibility to check that someone buying that bus ticket isn't a parolee and not allowed to leave the State, or George Stag's responsibility to ensure that the person renting that room is not a wanted fugitive in another State.
It's the police's duty to enforce the law. As I suggested uptopic, if someone's RKBA can be restricted due to a felony conviction, then so can one's 4th Amendment protections against search and seizure. Instead of making all the folk who are not convicted felons pay for this "background check" why not make a concerted effort to search and check up on the felons and see if they are in possession of arms in violation of their terms of sentence/probation/parole?
I want to be absolutely clear - I think all of the gun laws are bunk. Drop them now. For the responsible, law-abiding citizen they are of no value or purpose for their purchases and activities. However, I am not sure that the US is, on the whole, mature enough to deal with such a reality.
For most of our history, that was exactly the reality. The primary exception was various local "gun laws" intended by and large to keep "those people" in their place, things like making sure that the Night Riders and Klansmen didn't have to deal with armed opposition.
Beyond that, it's generally been "law enforcement" that has led to many of the problems we've had. For instance, the NFA was, in large part, a response to mob violence of the 20's, which was a result of Prohibition--the primary use of machine guns was to shoot up rival gangs property. Yes, there were some highly publicised murders using them, but mostly, property damage and intimidation was the goal.