Ryu, I think you are on the right track but it isn't working. When I click OK I get an Error Applying Security with the message "Failed to enumerate objects in the container. Access is denied." for each file in the directory.
Part of the failure may be because I can't follow your instructions. I can bring up the advanced security Settings for mIRC but I don't see an option to Convert inherited permissions into explicit permissions on this object. So I can modify the permission list but it won't let me apply changed permissions to the files.
I knew there was a reason I stayed away from ACLs all these years.