^^ That's the thing. The reference might always have been intended to be solely verbal and with no thought to actually showing the ship.
Maybe it's in the wording, but aridas
might simply be asking "what if?" MJ had been asked to come up with something.
Today, and even as early as second season's "Metamorphosis" we accept the idea early warp drive came into use sometime in the mid to latter 21st century. But as early as "The Cage" and during first season there was this apparent subtext that warp drive was a relatively recent (in universe) development. If we go strictly by what they seemed to be thinking early on then the Valiant
could likely have been quite primitive, But if we allow for a bit of retconning and look at it from the context of TOS' inferences as a whole then you have more creative leeway. And the latter is the approach I used for my design, but of course I could have tried for something even more rudimentary.
In my mind this also ties in to what Zefram Cochrane's prototype could look like. Suffice to say that I don't care at all for the design seen in FC along with all the stupid period world building that went with it.