A bonus to Natural Armor would stack with either of these effects, but they should not stack with eachother as they both grant the recipient a Natural Armor Enhancement Bonus.
Agree with Ted and Allyx - this is pretty clear; I don't know where some folks are getting the notion there's ambiguity on this. I mean, if you look hard enough there's always threads out there on the internets where folks will debate even some of the more clearer 3.5e RAW (this is one of them) - but just because one stumbles across such debates it should NOT muddle the picture. The 3.5e descriptions of natural ac, barkskin, and ammy of nat ac have always been quite clear afaik.
I just re-read the last entry I wrote … what was I smoking? Whatever it was, I promise to quit. Appears to cause brain damage. This is what I had intended to convey: In terms of “can’t hit you, can’t hurt you”, the combination of Mirror Image spell and Displacement spell is awesome. The attacker must pass three sequential dice rolls in order to hit, and the first two have nothing to do with how powerful the attacker is. First a concealment check from the Displacement spell(50% miss); then a mirror image check (random % of usually hitting the images); and then finally against the spellcaster’s AC. Not completely foolproof, but in all an extremely low chance of getting hit by any targeted physical attack. The spell Mislead is defined as a combination of Mirror Image + Greater Invisibility. However, this is how it actually works in ToEE: the attacker makes s single die roll against the special AC of the Mislead images, and a hit destroys the image. But as long as there are images dancing around, the spell caster is effectively untouchable with a 0% (zero) chance of even being targeted by a physical attack. Incidentally, this is how the 1st edition AD&D Mirror Image spell worked. Seriously: can’t even touch you, can’t hurt you.
True seeing and blindsight are 2 things from tabletop that can foil this combo, but mirror image + miss chance against you means targeted stuff misses often!
About Natural Armor Bonuses: While correcting this, I noticed that the fix for Righteous Might not stacking with the Amulet also caused Animal Growth not to stack the bonus with the animal's NPC AC Bonus. Will be fixed for next version, along with the above exploit.
Glad to see you're still working this... I'm trying a PF2e game, and not liking it much... It would be a HUGE pain to adapt to this engine (THREE actions per round, among other things).