Update: OK, long story short is that today I received a new IKA book as a dependent on my partner - yay!
For others in the same position, I post our experience here. When we visited the IKA offices initially with our new Cohab Agreement, we were told that this was not recognised and we needed an S1 form from the DWP showing me as a dependant upon my partner. Despite several discussions with IKA, we were told that without an S1 form Greece would be unable to reclaim anything paid out on my future medical needs. I spoke to the DWP and the fact that we had a Cohab Agreement was irrelevant to them; they simply asked if I was dependant upon my partner which I confirmed and they sent out an S1 form to myself and my partner indicating my dependance, which we received a few days ago.
This morning we visited IKA with what felt like a library's worth of paperwork but what in fact was asked for was: my partner's IKA book, a joint tax return (we only had individual ones but will in future have a joint one, so she accepted those), a passport sized photo of me, our passports. I was told that future renewals of our books could be done at a KEP office. My old pink IKA book was returned to me and a new green book was issued to me showing me as a dependant.
Just relieved that it's done.
Someday is now : )