Don't forget Friendship One, which would of had to of been making 200 plus the speed of light to have gotten where it was found. Probably faster if it was making frequent stops and not just making a bee line for the last planet it reached.
It was an uncrewed probe, so it probably didn't stop anywhere, just soared straight ahead through space. Also, with no need to use energy for life support, it could probably go faster than a crewed ship of the same vintage.
Wormhole? Star Trek said they're actually pretty rare.
It said stable, controllable wormholes were rare. The kind of wormhole we're talking about is the kind seen in ST:TMP, the result of an unbalanced warp field going unstable and out of control.
Enterprise was at odds with the previous series in terms of the Trek back history.
No more so than the previous series were with each other, or with themselves. TOS said the Third World War was in the 1990s, TNG said it was mid-21st century. TNG showed the Federation conducting genetic engineering openly in "Unnatural Selection," then DS9 retroactively claimed it had been illegal since Khan's time. TNG claimed that holodecks were a novelty, then VGR said that Janeway had played in them as a child. And so on. Trek history has been constantly retconned over the decades, and the "correct" version is always the most recent one, because that's how fiction works.
The explanation that doesn't stretch credulity to a breaking point is that Humanity achieved multiple hundreds time light speed propulsion fairly quickly after Cochrane's first flight.
Credulity is broken when you start pretending the information from later series doesn't exist. By that logic, you might as well talk about James R. Kirk and lithium crystals.