Polling would be good enough I would think here, do a poll and if you're within 10% of a majority being in favor, just do it and then let them decide on the final agreement. Be public with that stance so that the EU and the population know that the public will have the final say and we (the gov) aren't trying to railroad this

Maybe in a country the size of Iceland it's not as big a deal to run an election but it seems like a lot of work for what is just an advisory vote