There's not that many ways you can hack your trip to Iceland. One of the challenges is that almost every flight is on Icelandair, which has its own rewards program that I'm guessing almost no one listening to has points and miles that will get them in. The only exception to that is that they are a partner of Alaska Airlines.
And so you can book Icelandair flights with Alaska miles. Availability depends, but I couldn't find a single date that was available anywhere near when we wanted to go, even up till the day or two before in business class. Only economy. The planes themselves on Icelandair, I thought were fine.
They were new, they're modern. Business class was the same as you'd seen in a domestic business class. So you might think, do I really wanna splurge for this? And yes, you will get a bigger seat and more room, but you will absolutely not get a lie-flat bed like you would splurging for business class on almost every other overseas flight.
With the exception of United Airlines does have, and I think it might be the only, but things change all the time.