the aircraft accelerates in relation to the air mass under whilst the drag remains constant
After Mcrit there will be an additional drag component associated with shockwaves. Since all cruise Mach numbers are above Mcrit this wave drag will be encountered at some point during the latter portion of the climb. For something like the 737NG, if memory serves, Mdiv is within the 0.6-0.7 Mach range.
Mcrit is by no means limiting for transonic aircraft.
...TAS would always have to be increasing...
It will always be monotonically increasing except when a discontinuity in temperature with altitude is encountered. You'd need roughly a 30 K temperature difference per 1000 m to observe that exception therefore it will be quite rare.
The pressure altitude at which a given CAS corresponds to a given Mach number, called the crossover altitude, does not vary in the presence of a temperature deviation from ISA.
Here's a post from Old Smokey which might interest you.
http://www.pprune.org/tech-log/22598...l-mach-no.html