There is one other interesting thing, too. When Kirk and his landing party board the Botany Bay they find a gravity environment in place. Yeah, sure, they couldn't afford to show a zero-g environment, but it means the Enterprise crew have either advanced magnetic boots that look just like regular service boots or there actually was at least a minimal artificial gravity environment aboard the Botany Bay that kicked in when the presence of the Enterprise was detected. And since the Enterprise crew are showing much care in how they move aboard I think it argues that Earth science in Trek's 1990s had somehow developed at least a minimal form of artificial gravity.
I'd say that the Botany Bay had contant-on artificial gravity even before the Enterprise showed up, just based on the way Khan and his followers were just laying in their sleeper chambers without any restraints. And they couldn't have had their own magnetic boots either, since some came out barefoot. I doubt that would affect your artistic interpretation of the Valiant, in any case.