But...your immediate problem will be the airline you fly, they are responsible for verifying validity of the passport and may have policies that supersedes Iceland's requirements, or at least if they do not let you board, what Iceland thinks is moot.
So start with your airline, they may have an app on their website for you to enter pertinent information into to determine if they will accept.
A second issue is that Iceland, being part of the Schengen area, may consider requirements of partner countries if you are continuing on into the Schengen area.
In the end, if you have time, why not just renew now and eliminate any risk?