You are still subtracting twice (or 3x depending on how you want to look at it) in almost all cases. If a bugbear hits you for 8 damage, you subtract 3 from the armor pool, you then subtract 3 from the 8 damage, and then subtract 5 from your hit points. I don't see how this is faster than DR (subtract 3 from the 8 and subtract 5 from HP). Your system is at least as long, if not longer, to resolve.
Then I'm explaining it wrong. The armor pool grows by level, and disappears when used up. In your example, now that the damage has exceeded the armor pool, those 3 points are used up, and you don't have to subtract them any more until the end of your next short rest. Or, to change your example a little, suppose you're 6th level and your armor pool is 18 points; that bugbear hit reduces your armor pool to 10, and no further subtraction is required. In fact you could take another such hit (reducing armor pool to 2) without further subtraction. It's pretty much armor-as-temporary-hit-points, or armor-as-diviner-arcane-ward.