(For the readers: that's a 40 cal revolver that suuuuuucks to shoot and the drunk across the street is a real person, with a bunch of guns, who would like to buy it from me)
It depends on what one sees as reasonable. One might reasonably believe that the requirements for private sale background checks might not make an impact because there's no monitoring or effective enforcement mechanisms in the suggested system.
When we use qualifiers like reasonable or common sense, it's an attack on the other side and creates a divide between the debating parties. People should be debating the the proposed solutions and the objections to them.
People make choices about how they will respond to feeling vulnerable. Some people rely more on authority, for example, wanting more gun regulations. Some people will opt to go get a carry permit or purchase a weapon to protect themselves.
My point is that you are hoping that people who have already chosen the self-protection strategy will switch to the authority strategy for dealing with vulnerability. This might happen in a few rare cases, but it seems like you don't understand gun culture or conservatives in general.