I'm still sort of opposed to making the Copernicus
into a small, shipboard auxiliary, when she could more directly represent the "runabout" school of thought and be distinguished by the factors we already witnessed in the episode: a rather cavernous interior for long endurance, an overall size worthy of a long range vessel, and a complex stern structure that features exotic doorway arrangements and quite possibly also hides an elevator or a stair of some sort to allow our heroes to descend to the surface.
But if it's going to be a shipboard craft, the Copernicus
is probably best described exactly as you make it look: true to the general shape and feel of the cartoon art, but with the rounded edges and solid shapes familiar from the TOS prop. An impulse engine integrated into the aft hatch would probably be fine, considering the TNG "postcedent"...