"Tasty Mead" is the friend a lot of people forget; it reduces Health Regen, but increases your Stamina Regen. Great for your "Out of Combat" scenarios like mining.

If you're going through an area with a lot of mobs, don't rush through it. Take your time, and defeat the enemies one at a time, instead of getting surrounded and having your stamina (and health) draining scenario you mention. When you are at a point in the game where you are overgeared for the area, THAT is when you can just be a parkour king; not before.