Armour makes it harder to take your hit points away. I'd keep them separate to keep it simple.If hit points are abstract, shouldn't armor then increase your hit points?
This has to be handwaved to a point, unless people want to go more in depth with weapon tables. You can narrate the character shaking off the electricity somehow, or dodging the blow entirely. I'd like to differentiate between damage and weapons more, but I haven't found a way to make it worth the added complexity so I mostly ignore it.A problem also arises with damage types. For example, what if you are struck by a sword that deals electrical damage, while wearing full plate? The full plate should block the damage from the sword, yet the electricity damage should logically still hit you. And the game rules also make no difference between blunt and sharp weapons against armor. Most of the weapons in D&D just do damage. But obviously these different weapons existed for a good reason.
And the knight with padding underneath- I never even thought of that. I haven't had enough interest in armour to really see what they were made of or to reflect in my games, but it might be cool to read up on them.