I tried using hardcore restrictions, but found some of the really hardcore stuff, like playing without a HUD on, to be very tedious. While fun for a while, it gets annoying fast.
I always play with intermediate restrictions, though. Eating and sleeping regularly, only running when it is necessary, keep carry weight reasonable, health potions only at reasonable times/hand free, many of the same things as you, OP.
Also, I like to fight tactically, rather than just slashing my enemy to bits in a few seconds. Blocking, using shield to deflect arrows (makes me feel like a badass), shield bashing, taking strategic strikes, circling, all those sorts of things. Gives fighting much more depth and actually draws out some encounters. It's also fun to see how little health you can lose in a fight by dodging and blocking while chipping away at your opponent's health.