There's some basis for arguing that, after fiddling with all sorts of strange systems for four-digit registries in the 23rd century, Starfleet started with NCC-10000 in the first decade of the 24th, and then added a thousand units per year, or at least ten thousand per decade. That is, a ship from the late 2340s such as O'Brien's Rutledge would rightly have a 57000 range rego, while a ship from your time brackets might plausibly have something in the 60000-69000 range.
Known ships with registries like that include Nebulas, Akiras, Norways and some kitbashes of the Voyager, hence possible predecessors of the Intrepid class which culminates that design trend before the trend evident in Nova and Sovereign takes over. So, round, smooth lines, but quite possibly some spoonish rather than saucerish primary hulls, too...
IMHO, of course.
Timo Saloniemi