I'd argue limiting the ability to carry concealed by permit is a direct infringement on it's face. These are rights not privileges we get if we meet the criteria for a permit.
My guess is that'd be a losing argument. In a republic based on ordered liberty, all natural rights are subject to reasonable regulation. Regulating a right out of existence, however, is unreasonable and seems to be what the courts regard as an infringement. May-issue jurisdictions have essentially regulated the right to carry out of existence for most of their citizens.
As I recall, concealed carry case law, what little exists, was established in the 19th century in state courts, which consistently ruled there is no right to carry concealed. At the time concealed carry was regarded as sneaky and suspicious. Today it is carrying openly that is likely to cause a commotion — what is out of sight of the gun hater is out of his mind. This is why the 7th Circuit, when ordering Illinois to make carry lawful, gave the state the ability to regulate carry by permit and by limiting carry to concealed only.