I'm curious where you got the "late 22nd century" dates from? I can't recall anything stating that the Oberth type was around in the 2100's at all...
The 2200's takes place in the 23rd century, so I'm assuming this is a typo on your end.
That said, I take no issue with the Oberth type coming into being around the same time as the Original Connies, before the mid 23rd century (2250's). The numbering would be based on the contract so even if the Oberths where commissioned after the first Connies, the contract number for that range of vessels COULD have been lower than the 1700's. Then they jump up based on refit, or redesigns maybe? That would explain the higher numbers in the 24th century. New design based on an existing spaceframe, but a newer ship that required a newer contract number, and therefore the 5 digits.
In fact, that even explains the odd Connie with the NCC lower than 17's. That one would be the first, and that one would have that original contract number. But then something happens with the design for the Constellation NCC-1017 that completely changes the contract number, bumping them up to the 17's... Just a recycled thought. Precedent is in past naval history where ships are so upgraded and changed inside, that the class changes. Completely different ships (and planes) that look like the original. But in no other way are the same. Hell, even frames are upgraded, leaving just an original looking skin.