About a month back I spoke to one fellow who wanted to comply with the new law and who claimed he telephoned every sporting goods store close to his home to ask about private party sales, and was told they don't do those. I've even heard that a couple of gun stores would only agree to handle the transaction if the gun was entered into their inventory and sold on consignment for a percentage. It seems there's only about a dozen FFLs in the state who are doing these for the general public, they aren't advertising it, and some of those are by appointment only.
I don't believe this law was intended to be followed. I believe it was intended solely to criminalize collectors, hunters, and target shooters for doing trades. Even NY, which has some of the strictest gun laws in the country, does not require a background check for trades or sales of traditional hunting rifles, shotguns, and 22s.