Okay, just FYI: I also have been flying many years in an ICAO country and I keep 2 logbooks, one EASA and one ICAO, specifical for the country CAA. Both logbooks have the same hours, BUT all the EASA sims are only in the EASA logbook, not in the ICAO. The local CAA doesn't really need to know what I do in my spare time.
Keep in mind as well that, if you fly on a validation of an EASA license, the FTL that regulates your duty time is the EASA ones, NOT the local CAA ones. That could land you some trouble with EASA.
As a good habit, stick a copy of your local ICAO license on your EASA logbook to make sure any EASA inspector knows that you'll flew under another set of FTL rules.