So given the Enterprise (Constitution class), had a maximum speed of Warp 8, and a maximum safe speed of Warp 6 (As explained in TOS: That Which Survives), we can avarage that the Enterprise did a comfortable speed of 216c
Patently false, as our only datapoints into how fast the TOS warp factors are indicate speeds in the range of hundreds of lightyears in a DAY, not in a year.
We really can
forget all about that nonsense and start picking-and-choosing between actual datapoints, which may not be in complete agreement with each other but certainly debunk the idea that a nearby star could only be reached in a week. After all, Kirk in TOS hopped from star to star in a matter of days at the very most, without indication that those would be neighboring stars.
speeds would allow for the galactic hedgehog to extend its spikes across a thousand neighboring cultures easily enough in the couple of centuries the UFP has existed before Spock's World
. And that only by using the frontline starships; lesser probeships could also establish contact, or at least make others curious about the UFP and cause them to make contact.