Okay, a revised list, with some non-canon additions for fun:
2160s(?)
NX-class refit
Daedalus-class
2170s(?)
Bonaventure-class
2190s(?)
Baton Rouge-class
2200s(?)
Walker-class
2220s(?)
Einstein-class
???-class
???-class
???-class
2230s(?)
Constitution-class
Saladin-class
Antares-class
2250s(?)
Shepard-class
Cardenas-class
Crossfield-class
2270s
Constitution-class refit
Miranda-class
Constellation-class
2280s(?)
Oberth-class
Excelsior-class
Notably, if this sort of order is correct, registry would not seem to correspond at all to the apparent age of the design - the Saladin class has a three digit registry - the Mayflower, Newton, etc, types have registries higher than the newer USS Enterprise - so this lends substantial credence to Tuskin38's interpretation - and would lend a lot of evidence to the idea registry represents something different to production number - in the past I thought registry generally represented age, but something like this:
Perhaps the original contract of 12 ships bear consecutive registries (and that the reason for lower numbers on later ships is because other shipyards were awarded contracts to build ships prior to their contract being sent) - obviously this is for fun and has no basis canon:
Batch 1 (San Francisco Fleet Yards):
USS Constitution NCC-1700
USS Enterprise NCC-1701
USS Hornet NCC-1702
USS Hood NCC-1703
USS Intrepid NCC-1704
USS Independence NCC-1705
USS Franklin NCC-1706
USS Midway NCC-1707
USS Iwo Jima NCC-1708
USS Lexington NCC-1709
USS Yorktown NCC-1710
USS Wasp NCC-1711
Batch 2 (Antares Fleet Yards):
USS Constellation NCC-1017 ???
USS ?????????? NCC-???? ???
Batch 3 (Utopia Planet Fleet Yards):
USS Potemkin NCC-1659 ???
USS ??????? NCC-???? ???
USS ??????? NCC-???? ???
USS ??????? NCC-???? ???
USS ??????? NCC-???? ???
USS Excalibur NCC-1664 ???
Batch 4 (41 Eridani Fleet Yards):
USS ????? NCC-???? ???
USS Exeter NCC-1672 ???
Batch 5 (San Fransisco Fleet Yards):
USS ?????? NCC-???? ???
USS Defiant NCC-1764 ???
Batch 6 (Utopia Planetia Fleet Yards):
USS ???????? NCC-???? ???
USS Endevour NCC-1856 ???
But where that made a fair bit of sense, perhaps the registry does not even represent contracts, but something more like what I once saw suggested by someone else once - like a component of two numbers - the first two digits represent the first two digits of an appropriations bill, or the last two digits, or something - and the second represent the production number within that bill. I dunno if that makes sense, just throwing the idea out there:
Federation Council / Appropriations Bill SC-098-05 - Stardate 2223:
Batch 01, Ship production number 14, San Francisco Fleet Yards
USS Kelvin, NCC-0514
But then that also would not explain the production numbers of some of the Constitution class ships in official canon, so I guess some combination of the two systems might make sense, or there are more than two components to the reigistry:
Federation Council Appropriations Bill SC-H76-117
San Francisco Fleet Yards Contract XGY98-00
Build at Earth:
Ship 1: USS Constitution NCC 1700
Ship 2: USS Enterprise NCC 1701
Federation Council Appropriations Bill SC-H76-216
Utopia Planetia Shipyards Contract XFS09-72
Built at Mars:
Ship 1: USS Exeter NCC 1672
Ship 2: USS ?????? NCC 1673
Federation Council Appropriations Bill SC-H76-310
41 Eridani Shipyards Contract HYU17-16
Built at Vulcan:
Ship 1: USS ??????????? 1016
Ship 2: USS Constellation 1017
Or with shipyards having a rolling counter that re-sets every hundred maybe? I dunno, just throwing some ideas out. Maybe like warp scales, they were re-calibrated to a five digit number before TNG, except where ships had a special lineage like the USS Enterprise.