Robert,
As already mentioned, the time it takes to create this category and then certify aircraft within that category could be long enough that the specification may be outdated before it is used.
Rather than defining a new category that captures some of the improved precision now available, why don't you start at the beginning, determine a level of instrumentation performance that is required to reduce minima, reduce seperation, and/or increase traffic volume, and then define a category that meets those criteria?
For altimeter setting errors, I think most of those would be eliminated if the METAR was also transmitted digitally, and the aircraft announced if the aircraft altimeter settings differ from the one transmitted. Temperature correction errors could also be mitigated.
Height loss on overshoot is not something I've considered before. However, I have worked on height loss following engine failure with a second engine intentionally shut down. So many factors were involved that one solution wasn't possible, but applying a height to each factor was straight forward. Perhaps this approach would work for your specification. One aircraft might have excellent altimetry, but poor OEI climb performance. It may also be possible to apply reduced height loss based on procedures or training.
I have little else to add onthe content of the definition, but I would avoid the term "new advanced aircraft" and just focus on approach instrumentation performance.
Cheers,
Matthew.