Also, there is no onscreen evidence to suggest that the Mirandas existed in the time before TMP.
I say this depends on what you consider onscreen evidence.
In one of his Enterprise pre-production sketches Matt Jefferies stated that the "17" in "1701" referred to the Enterprise
being a member of the 17th Federation starship ("cruiser" in the TOS pre-production stage) design series.
By that logic (from a TOS and TOS movies' point of view) that would make the Reliant
(NCC-1864) a starship of the 18th design series.
Interestingly and "thanks" to HD resolution, the starship status chart in "Court Martial" clearly identifies the erroneous NCC-1631 to be actually NCC-1831
Thus, IMHO, there is TOS evidence that the 18th starship design series (i.e. Miranda Class) already existed during the era of TOS but, of course, remained unseen.
It is my belief (I wrote an extensive treatise on the subject) that the Oberth Class is actually much older than usually assumed and the missing design link between the Miranda Class and the Starship Class the Enterprise
and her sister ships belong to.