Also, there is no onscreen evidence to suggest that the Mirandas existed in the time before TMP. In fact, if the Enterprise refit was a testbed for a bunch of new technology and ideas (as seems to be the case), then it's very likely the Mirandas were entirely new ships grown out of that leap.
That would put their origin around 2280 rather than around 2245 or so.
The thing that always intrigues me is we then see a bunch of Miranda class ships with NCC numbers in the 20K-32K range - build numbers from right around the same time as the Ambassador class and its variants come into play. This combined with the very few numbers of Ambassador-class ships suggests, at least to me, that the Ambassador and Ambassador variants were all fairly unsuccessful so Starfleet looked to some older, more proven hull types like the Miranda to lean on as support ships. That could also be the case for the Oberths, which we see pretty far into TNG's run and even a bit into DS9.