D&D 5E Trading AC for DR in 5e

This is what I would go with based on the system I posted earlier.

Padded: 6 bonus HPs; AC = 10 + Dex.
Leather: 6 bonus HPs; AC = 10 + Dex.
Studded Leather: 12 bonus HPs; AC = 10 + Dex.

Hide: 12 bonus HPs; AC = 10 + Dex (max 2).
Chain Shirt: 18 bonus HPs; AC = 10 + Dex (max 2).
Scale Mail: 24 bonus HPs; AC = 10 + Dex (max 2).
Breastplate: 24 bonus HPs; AC = 10 + Dex (max 2).
Half Plate: 30 bonus HPs; AC = 10 + Dex (max 2).

Ring Mail: 24 bonus HPs; AC = 10.
Chain Mail: 36 bonus HPs; AC = 10.
Splint: 42 bonus HPs; AC = 10.
Plate: 48 bonus HPs; AC = 10.

Shield: I might go with either +2 AC or 12 bonus HPs. Neither are what I would prefer. I think shields are probably best as granting some kind of cover (but that's a different mechanical concept).
 

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Bonus HP either in temporary or real hit points added to your current total when you don armor would amount to the same thing if D&D only consisted of non-magical weapon combat, but it doesn't.

It's not balanced with the base system because adding HP means your armor effectively would add points of AC to all damage from falling, drowning, spells and saving throws that more often than not, do not have their expected damage altered when you are wearing armor. There is no reason to use DR if you aren't using it to have a more realistic combat engine. DR is simulationistic. Any system implementing DR should therefore not make armor make you take longer to drown, for example. Or mean that getting touched by a disintegration spell would work less. If that's how you want the spell to work, where armor disintegrates first, that's fine, but it's not how the spell works as is currently written. Power word kill would need to be re-written, as would many other spells.

Reducing incoming damage on a case-by-case basis is really the only way here. It's easy to make up a system that works in a void if you were creating the edition over from scratch, but trying to make a DR system that's balanced with the base system is something else entirely. For example, I don't see why HP added when you don armor wouldn't work generally, including for fireballs and lightning bolts, but that's not the same game and is a huge boost to the value of heavy armor. Maybe that's a good thing, but it's not balanced and can't be used like the OP wants, for one player but not the rest. It is tanky feeling. I like it and it's the easiest and fastest way to do DR in game (faster than even a lookup table), but it's not balanced. A lookup table can also amortize the overhead of using a DR system in many instances, such as %-based DR + resistance/vulnerability + heavy armor master feat all at the same time. You just print out another column for your armor type for each case. This would still be much faster than even the current system for players with damage resistance (50% DR) + heavy armor master absorption (DR 3). You just update your chart when you take the heavy armor master feat, then keep playing the exact same way. The first three values (at least) in the table will then be 0.

I do however like that so many people are like me and want D&D combat to behave more realistically with simulation in mind. Heavy armor users are slower and easier to hit and damage, but take less damage than those who do get hit with less armor (though they get missed entirely less often). It's a better and more accurate damage model, since it does not require you to average out many hits and misses to model the case where you're hit, but it hurts less than it otherwise would.
 
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...Any system implementing DR should therefore not make armor make you take longer to drown...

I would actually point out, regarding this, that drowning in 5e does not deal damage to you - when you run out of breath your HP is set to zero, regardless of how much you have. On your other points, I feel like most of them would be avoided by tracking armour HP separately from regular HP when it is considered relevant. If we are talking about the proposal of certain amount refreshed each turn as was suggested earlier, at least, you'll need to separate the two values anyway.
 

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