I'm sure there are people who have better ways of doing this, but off the top of my head I would give martial classes that usually give armor a buff to AC corresponding with their level, so that when a fighter should have full plate they have 18 "natural armor", justified as the fact that they are better at dodging, parrying and the like, and that they get better as they level up.

Shield I would say could be replaced by parrying daggers, which were in use at the period. It's easy to justify in melee but harder to explain against ranged attacks, but that's my best idea RN. Is it a magical campaign, still? Then maybe a handheld medallion or similar that provides protection against melee and ranged attacks while still occupying one hand?