In the EU Iceland would lose sovereignty because the EU is going federal, and the people of Iceland would lose sovereignty, too as a consequence. You are trying to clutch at straws because you are insisting on denying a fact that is not even controversial. I understand that you think it is worth it but not you should deny it is the case.
Iceland is in the EEA (and indeed that's already a loss of sovereignty) not in the EU and a key reason is indeed to maintain sovereignty on key issues and industries (especially fishing, which is excluded from EEA), which they would lose by joining. So again it is very unclear to me what they would gain by joining.
Why would they lose sovereignty? You haven't established that at all.
If we read Rousseau's Social Contract, we see that the sovereign is the people, not the executive power at their service.
The people wouldn't stop being the sovereign just because they change the administrative details of executing their sovereign will.
You haven't made a successful case to counter this point, instead you've gone to attacking me personally with loaded language ("clutching at straws") to defend your insularism.
Sovereignty, noun: the power of a country to control its own government. [Cambridge]
A country, EU member, Euro, Schengen, etc. does not control its foreign trade, has no currency, does not control its monetary policy, does not control its borders (Iceland is a remore island so possibly less of a practical issue and indeed they are in Schengen), does not control its laws. That's the way it is. This includes the people as citizens of that country.
I think you are trying to say that they are still "sovereign" at EU level but obviously that's fallaciously ignoring the whole actual issue of national sovereignty vs. the EU, which isn't just a "change of administrative details", obviously...
Interestingly, with your argument they could equally join the US and as long as they have full voting rights they would still be "sovereign", which I don't think many would agree they would be because the whole point is obviously being sovereign as Iceland and Icelandic, not as citizens of whatever other country.
That's the issue with discussing the EU within Europe at this point, it has become a religion and it is not possible to discuss religion with religious people.
Iceland is in the EEA (and indeed that's already a loss of sovereignty) not in the EU and a key reason is indeed to maintain sovereignty on key issues and industries (especially fishing, which is excluded from EEA), which they would lose by joining. So again it is very unclear to me what they would gain by joining.