Thanks for the offer, Polar_S, but my schedule is chaotic in the extreme these days!
If your MEP Rating is less than 5 years lapsed, all you should be required to do is to take a MEP Class Rating Proficiency Check (LPC SPA) which doesn't have to be conducted by a 'Staff FE' - in fact a suitably qualified UK/FE(PPL) could do it. The only training neded is whatever you and your FTO think that you need in order to pass the Proficiency Check and the Examiner can sign your licence then and there - a new form called FCL150CJAR 'Ratings - Certificate of Revalidation' goes in your licence and all Examiners have stocks of these.
It is only because you are also renewing your IR in section 3B (if you so choose) and the fact that it's between 5 and 10 years lapsed that you need a 'Staff FE' to conduct your single check flight. You can, if you wish, just do the MEP renewal with a non-Staff FE and then do the multi engine single pilot IR with the Staff FE on a second flight. I advise that you check the comparative costs though!
Don't let the Belgrano give you bad advice, to summarise, tell them:
1. Your MEP rating is less than 5 years lapsed, therefore you only need to renew it by completing a LPC SPA on a MEP aircraft.
2. Your IR is between 5 and not more than 10 years lapsed, therefore you will need to renew it with a Staff FE - you do NOT need to fly another initial IR.
3. Should you wish to renew your IR by doing it in Section 3B of your MEP renewal LPC SPA, what would the Authority's fee be for conducting the combined check.
Hope that this helps - do let us know whether they still don't agree as this is all in the CAA FE's handbook and they must know that!