I think I am well on the way having finally established the right overall look. Now it's more detailing and finally colouring.
Although I don't actually use a 1960's rocket to build on the rocket influence can clearly be seen. To a 1960's audience this would evoke a rocket yet not like one they have actually seen. And they would surely wonder what the rings were about given they are far too thin to be habitable. And this design looks to have a sort of tail fin, but it's far too thick and there is only one of them. I think it clearly looks like some sort of powerful rocket shape yet suggesting something much more advanced than anything they might have heard of or read about. And it doesn't look
Buck Rogers,
Flash Gordon or 1940s-'50s sci-fi although perhaps something similar might have graced the cover of a pulp sci-fi novel or magazine.
I have tried to integrate Matt Jefferies' general ringship concept with a vaguely 1960's rocket booster shape as well as the general sense of TOS' established aesthetic as reflected in the TOS
E, which was really the only major example of
Star Trek design in 1965. I have also tried to avoid obvious post 1960s science fiction and real world aerospace influences.
When the space warp was discovered in the mid 21st century what sort of spacecraft could Earth have been flying then? Note that we are free to ignore TNG's post atomic horror and their take on Zefram Cochrane and 21st century Earth. In WNMHGB we have not yet learned of the Eugenics Wars although the idea of a third world war was something people then might have thought was yet again possible in the future. We haven't learned of sleeper ships yet or Zefram Cochrane.
People of the 1960s likely would have thought that space propulsion would steadily improve over the coming years and decades. Science fiction in print and film had already spread the ideas of interstellar travel and even suspended animation. The idea of relativistic ships reaching high percentages of light and thus taking advantage of time dilation (in hand with suspended animation) were popular ideas floating around at the time and not considered unreasonable within the coming decades.
When the space warp is discovered and FTL made possible and practical the first ships might not have been clean sheet designs, but rather adaptations of existing design concepts, much like early automobiles still evoked horse drawn wagons and early steamships still evoked wind driven sailing ships. Thus Earth's early FTL ships could have been based upon existing relativistic vessels.
And a design like this, while looking suitably advanced compared to 1960's chemical rocket boosters would still look outdated compared to the exotic looking
Enterprise.