I will have a go at the reply - not sure if I am correct, so it will be interesting to hear other better informed views.
Your FAA license entitles you to fly G reg aircraft, but without IR or night privileges. Your FAA license will entitle you to a JAR license, and your IR to a CAA IMC, all of course subject to application. Your FAA IR does not entitle you to a JAR IR, and the CAA will specify what additional training is required.
Your JAR MEP is just that and does not give you license privileges on a SEP.
Presumably the CAA can direct what additional training you would require to add a SEP, but then again presumably it would be granted by right on the strength of your FAA SEP.