All of the above sounds fine in general terms, yes, turbine engines do decline in thrust as altitude increases, but................
Point 1. A great many jet engines are 'flat rated', i.e. Pressure Limited, and this pressure limit prevails to an altitude where there is insufficient density to produce the pressure limit, and are, thereafter, 'Full Rated' or Temperature limited. Thus, up to the level where the Flat Rating prevails, thrust will be constant, and, to take it one step further, thrust may INCREASE due to lower back pressure from lower ambient atmospheric pressure. I know of at least one engine that is flat rated up to 8,000 feet.
Point 2. If the Net thrust remains constant, as alluded to in Point 1, the EAS for Vmcg will remain the same. For a constant EAS, IAS or CAS will be
HIGHER.
Having said all that, the Vmcg for certification purposes is calculated for the WORST CASE, and not the prevailing case, thus the official Vmcg published in the AFM will be the same irrespective of the Altitude.
Did that throw a spanner in the works?
Regards,
Old Smokey