I've been doing similar research recently.

Delta flies JFK-KEF so if you have ways of getting some miles into that account, you may be able to use them on that route. Of course, availability with Delta is an entirely different story.

Short of that, staralliance is probably the only other mile-based way but I find it difficult to justify sitting on the plane twice as long and essentially backtracking from continental Europe back to Iceland and repeating that again on the way back when I can pay usually sub-$1K and be there in maybe 6 hrs.

Somebody else also recommended tours to me as a good way to save when traveling to Iceland.