On the up side, no matter how bad the booking process is, Icelandair handles wheelchair assistance very well at KEF. They are efficient and friendly, yet don't assume you are mentally deficient just because you need help getting around. (In my personal experience.)

KEF was also an airport where they were happy to let my spouse push me in the airport wheelchair if we wished, which we do like because we can stay flexible about lounge vs. gate and move on our own timeline.