Thus, I don't find it credible that they would use the same sets for two such incompatible purposes.
I find it completely credible that they could use the same set for that purpose. The new set is designed to look very similar to the original set. It should look similar in either production, which serves the purpose of both productions.
If they are to show the original console room in Doctor Who proper, it'll look lower tech and less glitzy than what we've got now because that's how it actually looked onscreen in early Doctor Who.
The two goals are entirely compatible because they both require sets that look like the original console room.