I am struggling to understand the OP's point/question. From the point of view of the ground equipment there is only CATI, II, IIIA, B & C. I am not aware of there being any other subclassifications as mentioned by the OP taking into account various other factors that are not pertaining to the capability of the ground system, e.g. autopilot capability etc. Aircrew will already be fully aware of the capability of their aircraft/avionics and how that affects thir ability to fly published procedures and with the specified minima.
Here in the UK (and everywhere else IIRC) any reduction in ILS CAT will already be published both by NOTAM and broadcast on the ATIS. Aircrew, ATC and Tels will already be fully aware of ILS CAT and the related minima at any given time anyway, so I don't understand the point being made here - there wouldn't be any need to discuss the ILS capability on RT if its already known, surely? I have never heard ATC or Aircrew discussing this on-air before.
Smithy