D'Addarios are the recommended string for Avalon, Lowden and McIlroy. so they should be fine, A lot of players on here use 13s and 12s, so you should be OK if you stay in that range - no heavier than 13s, though!
A loose brace can cause buzzing - I guess your luthier checked for this?
Keeping the guitar in the case is good, but even better when there is a humidifier inside. Planet Waves make good cheap ones. As a temporary measure put a damp sponge in a plastic bag with a few small holes in it inside the case. (Not too wet, just damp!)
Half the fun of owning a solid wood guitar is tweaking to get it just right! Good luck!