This. Or look at the unarmored AC boosts for barbarian and monk.
Barkskin isn't just a slight difference in phrasing, that can be chalked up to natural language. It's dramatically different. As I interpret it, then, anything that adds to your AC simply has no effect while you're barkskinned until it exceeds 16. Thus:
Barkskin = AC 16.
Barkskin + Dex 20 = AC 16.
Barkskin + shield = AC 16.
Barkskin + mage armor = AC 16.
Barkskin + shield + mage armor = AC 17.
Barkskin + mage armor + Dex 20 = AC 18.
IOW, your AC is either determined by barkskin or by everything else, whichever is higher.
Could you clarify by editing with red and green font eventually which parts of the armor do contribute in each case please?
Ups i fell for a case of slight thread necromancy sorry for my zeal.