AC from Dexterity vs. AC from armor
Your Dexterity bonus to AC is vastly superior to your armor bonus to AC, because your Dexterity bonus applies against touch attacks and your armor does not. That makes bonuses from Dex twice or more as valuable as bonuses from armor. Thus, even if the total AC ends up being lower, the mithral breastplate is probably better defensively—and that’s before we even get into things like movement speed and armor check penalties.
Mithral breastplate vs. even lighter armors
Honestly, it’s entirely likely that your best option is actually a mithral chain shirt or darkleaf lamellar leather, rather than a mithral breastplate. Those have even lower penalties and even higher max Dex. I realize that takes you away from the Dex+heavy armor theme you had going on there, but at higher levels a +5 Dexterity bonus is rather poor for a Dexterity-focused character–you are quite likely to exceed that by a considerable margin, and therefore may very well reach a point where the lighter armor would be better than the mithral breastplate. This does depend on how high in level you expect to get, how likely you think it is that you’ll be able to trade your (heavily enchanted) mithral breastplate for an equivalent light armor, and so on, but in many games my preference would be for a lighter armor.
About AC in general
This is a “trap” in Pathfinder (and its ancestor, D&D 3.5e) that a lot of new players fall in, because the game makes AC out to be your first concern for defense. AC is the worst defense in the game. You should not focus very many resources on it.
It’s often claimed that the “Big 6” magic items that every Pathfinder character should get include three separate AC-boosting items, that is, a ring of protection and an amulet of natural armor on top of magic armor. A +5 armor, a ring of protection +5, and an amulet of natural armor +5 costs a staggering 125,000 gp. That gold gets you +15 AC, +10 of which doesn’t apply against touch attacks. And after all that, your AC is likely still mediocre, at best, and you’ll still be hit by most attacks.
Meanwhile, attacks almost always deal hp damage, which means even if you are hit, you have some wiggle room before it really matters. If you fail a saving throw, you are—at best—out of the fight. At worst, you could be turned against your allies. That makes your saves vastly more important to increase. And 125,000 gp can get a lot of saving throw bonuses, a lot of heavy resistances or immunities, and a lot of alternative protections even against attacks, like miss chances. It’s vastly cheaper to get a 50% miss chance than it is to get AC high enough that high-level foes are going to miss 50% of the time.
So the correct (optimal) thing to do for most Pathfinder characters is to get a +1 armor, and then ignore AC from then on. Maybe a ring of protection, since that covers (far more dangerous) touch attacks, though it’s also very expensive so you probably don’t want to go beyond +1 or so. Other defenses are more effective and vastly less expensive.
Anyway, if you really do want to get high AC, a high-Dexterity build is mathematically your only hope. With high Dexterity, you still have to spend a ton of gold—gold that may very well be better spent elsewhere—but at least by the end of it you have respectable AC that may actually pose something of a problem for enemies.