Why not simply give PC's an extra encounter power instead?
(I wouldn't make this into something you'd do instead of second wind. Having to give up your attack for the round is hard as it is - SW doesn't need any more drawbacks IMO)
I agree that Second Wind is often unused as it is. I also worry about odd exceptions, where you have an Encounter power that does 4W damage, versus an At-Will which does 1W + some effect, though maybe the lost healing balances out.
Finally, I believe there's a high level Warlord Utility (and I'm sure there are others) which grants another use of an expended Encounter power. It is a daily and costs a standard action.
Either way, I do like the name, I also like the fact it costs a healing surge, though it may change the nature of healing surges (and healing) to a certain extent. In order to prevent this change, I might go against my initial thoughts and have it be something you do instead of Second Wind, HOWEVER, it costs two standard actions. That is, a standard to regain the power, then a standard to use it. If a high level Warlord daily requires the same, giving everyone a similar encounter power seems like it should follow suit!
Off the top of my head, I am trying to think of when it would be worth it to do this. Certainly the Barbarian's Avalanche Strike might warrant this, or other classes who are typically single target damage but have a burst Encounter power. Or powers which have potent, if conditional, effects, such as the Cleric's Level 7 Encounter (potentially) multi-heal. Potentially abusable with Stun-style powers versus Solos, though with Elric's Saving Throws for Solos change that allows saves versus Until the End of Your Next Turn effects and so on, I think it'd be alright.
The fact that it's per encounter and costs a healing surge should prevent the tendency WotC saw for players to simply recharge and spam the same encounter powers.
I am wary of allowing Dwarves to minor then standard to unleash an Encounter Power, so I'd probably call this independent of their Dwarven Resilience, especially since it doesn't fit the flavor of Dwarves quite as well as Second Wind.