I think per-round DR is nicer than per-attack for some of these issues. It means that coordinating attacks (and doing things to prevent attacks from being coordinated) becomes more important.

I guess the way I'd do it is, attacks have almost 100% hit rate by default - you're rolling d20+Dex modifier against an AC equal to the target's Dex modifier and thats (mostly) it, which means mostly you're looking for crits or natural 1s. Monks and Rogues get to increase their AC with level-scaling bonuses when wearing no armor or light armor respectively, with the Monk bonus capping out at 60% evasion against an equal Dex attacker and the Rogue bonus capping out at 30% (but these would stack if you cross-class). Maybe magic items or some spells can also fiddle with this, but leaning towards attacker Disadvantage rather than directly adding to the AC. Ring of Protection probably has to go away.

But now you have per-round DR from your armor instead, equal to say your Proficiency bonus (if proficient in the armor type) multiplied by 1 for light armor, 2 for medium, or 3 for heavy. If you aren't proficient, you just get the 1, 2, or 3 base value. Magic item plusses add to the effective Proficiency bonus being applied, so a +5 plate mail would give you a flat extra 15 per round soak. Sneak attacks and critical hits bypass this DR. Maybe some special things could 'break' or 'restore' this DR pool in multi-round fashion? You could have 'sunder' type mechanics but instead of destroying the item they do half damage but the DR pool cap is lowered by the damage dealt until repairs are made...

Tempted to let armor also block elemental damage with this DR, except perhaps certain thematic vulnerabilities - plate varieties are vulnerable to electricity and cold, chain/ring to acid (gets through the gaps), padded armors to fire, and scale and leather and splint are fine against all elements? Maybe necrotic gets through everything? Dunno... I'm also not sure where I want shields to go in this picture - I feel like a reaction to replace your AC with 5 + the shield's AC rating (rather than stacking) for the rest of the round could work but its a little messy, with early shields being worthless and stuff like +5 shields being way too good... Spells that would grant AC instead temporarily boost the DR pool for the round, or give Disadvantage to the attacker's roll.

Gotta rebalance some class features. There's stuff based on advantage on attack rolls or things like that, which is a lot less relevant with this. Reckless attack could just be 'deal 25% extra melee damage, take 25% extra melee damage', upgrading to 50%/50% at a later level. Unarmored Defense would give extra DR pool based on your Constitution rather than giving AC. Defense fighting style maybe upgrades the armor proficiency bonus by +1? Protection probably should just let the Fighter use their shield on someone else's behalf. Archery maybe just becomes a damage bonus? Case by case...