We do have canon evidence of crews as small as seven, and as large as 80. Googling for "USS Thagard" should provide you with an idea of how 80 could be rather easily packed aboard while still leaving room for meaningful gear (although I think the gear aboard the Thagard is a bit excessive).
On the registry number issue, I'd like to think that Starfleet when founded in the 2160s slapped registries from 1 to about 400 on its existing ships (which at the time didn't necessarily include support types - those got TAS-style, letter-prefixed registries instead). Those lasted for a while, and the 500 and 600 ranges only came to use on the dawn of the 23rd century. At that point, Starfleet decided it wanted to identify combatants by their registry numbers, and created a (rather half-baked) system where cruisers got 1000 or above (explaining the fandom Horizon class and other such stuff), destroyers and similar small types got 500 and beyond (like we see in FJ's manual), and in-between light cruisers and whatnot got 700 range registries (again explaining some fandom stuff). Such a system was of course doomed to become hopelessly confused, and about halfway through the century, Starfleet simply forgot about it and started filling the gaps.
The 600 range registries of early Oberths could well mean those ships were filling gaps left in the creation of older ship types, in this case large scouts such as the Hermes series. They need not be quite as old as the registry "suggests" - because the "suggestion" only works in the scarce material of canonically known registries. Fandom registries are not chronological for the 23rd century, and believing in those actually makes it easier to imagine backstories for some canon ships...
Timo Saloniemi