There is the S.S. Beagle. A small class-IV stardrive survey vessel that had a crew of 47, which was either a Intrepid type, a Neptune class or Oberth.
Nice catch! Of course, we do not know what type or class this vessel was. But obviously it was a "survey vessel" and the crew size may be compatible with an Oberth Class of Kirk's era.
Unfortunately I haven't done the math how many people could comfortably fit into the primary hull, but it's probably not that much taller than two decks at 395' overall length.
What makes you think that civilians could afford better ships during the TOS era?