I still like the Spaceflight Chronology's timeline.
Most references in TOS are in the two centuries/200 years range. Later, TOS in the 23rd century was confirmed.
The SFC handled it by placing the five-year mission around 2207, with TMP in 2215.
This way, TOS rough estimates of "two centuries" and "200 years" remain valid, while technically TOS is in the 23rd century.