From the YouTube clip, <i>Discovery</i>'s registry number is NCC-1031, so I'm thinking it would be much older than the post-ST:VI period.

The timeframe you're talking about might make sense other than that. ISTR relations between the Federation and the Klingons improved after the <i>Enterprise</i>-C was lost defending a Klingon colony from Romulan aggression.

Another thought: most of the simpler, blockier ship shapes seem to be earlier in the ST universe's history.

>Or maybe they could get the guy who modeled
>this
>to overhaul the Discovery.
>
>Although I'm liking the crazy fan theory rumor that the reason
>Discovery looks so chunky and Klingon is because it's a sort of
>joint venture between the Federation and the Klingons, set between The
>Undiscovered Country and Next Generation.
>
>"This is probably a stupid question, but . . ."