If you want to do IR in Iceland, you will have to have an Icelandic issued licence, those are the rules.
You can not go and do IR in Iceland, and CAA UK issue you their IR!
However I doubt very much Iceland will approve you to do the IR with ATPL's from Italy anyway, you have already it seems got the permission once to change to the CAA UK.
It is pretty simple, Iceland IR - Iceland licence, believe me I know this, because I have gone trough all this myself, I used to have a Norwegian licence.
Your first call would be Iceland CAA, that will pretty much tell you all you need to know.