Iceland Air. Still a budget airline but a little better than Wow I think. Carry on luggage is free unlike Wow. The price is great and the flights are direct. Great point about using the CSR for DH's ticket too. The insurance still works even when booked on points? We could use Capital One to offset the cost of lodging.
I thought I'd share my experience using Chase UR and AmEx MR to fly IcelandAir in July.
I transferred Chase UR points to Alaska miles for our outgoing flight. After purchasing IcelandAir tickets with Alaska miles, I was able to select seats on the IcelandAir website. All of the seats purchased with Alaska miles were Economy Standard and included a free checked bag.
I payed for our return flight with AmEx MR points, and I purchased the flight on the AmEx travel portal. After purchasing tickets, I was able to select seats on the IcelandAir website. Unfortunately, the seats via the AmEx portal were Economy Light and required an extra payment for baggage. At the time, I could not find a way to purchase Economy Standard via the AmEx travel portal.
Also, you should know that IcelandAir used to have 3 seating classes, but now there are only two - Economy and Saga. Even though there is only one Economy Class, on their narrow body jets, the first six rows of economy have much more leg room than the rest of the plane. (It's like Economy Plus on United or Delta Comfort+.) I was able to select these seats for our flights regardless of whether I purchased Economy Standard with Alaska miles or Economy Light with AmEx MR points.
********Edit on 8/22/18, 2145 cst********
Sorry, but I must apologize about an error in my earlier post. I completely forgot that my transfer of Chase UR points to Alaska required a hack that significantly changed on 6/5/18. I learned about this technique after the ending date had been announced, so I never shared it here or anywhere else. Feel free to read on for details, but understand that this hack doesn't work the same way any longer.
Prior to 6/5/18, if you booked an Alaska Airlines flight directly from AlaskaAir, then cancelled the flight on the Alaska Air website more than 36 hours after purchase *and* more than 60 days from the scheduled flight, you were given the option to refund the entire cost of the flight to Alaska's, "My Wallet," without any penalty. You could then use those funds to purchase a different ticket on any Alaska Airlines flight or any partner flight, including IcelandAir. I used Chase UR points to purchase dummy tickets on Alaska in approximately the amount needed for my IcelandAir flights (at 1.5 cents/point), then cancelled the dummy bookings, then purchased our IcelandAir tickets. It was pretty slick.
As of 6/15/18, you can still do this, but there is a $125 fee unless you have gold status with Alaska. I guess it might still be worthwhile if you have a companion pass on Alaska, but I haven't tried that personally, and I haven't read about it either.
********Second Edit********
OK, I haven't tried this but you can still use this strategy if you purchase a higher priced refundable ticket rather than a nonrefundable ticket.