Hi,
Short answer to your question: Yes, you are correct.
Just do the 6 hrs, 12 takeoffs/landings, and the 1 hr instruction flight (or any other PC/ST), and you are home free. Then to the paperwork:
Just how to enter the new expiry date for your SEP-rating physically/administratively speaking, differs between JAA states. Some states will allow for you to take your logbook with the hrs/lndgs/instruction flight, and find an examiner who can then enter the new expiry date. Some member states will insist you send your paperwork to them for entering the new date. And some states will allow both. So you will just have to find out what administrative procedures are in place in your state.
Cheers,
Redbar1