Would vutpa' DungDaq 'oH Qe''e' (without the taH) also be correct in this case?
Yes. And probably even better, since the restaurant is (more or less) permanently above the kitchen.
However, that alternative was not in the list of accepted ones; I've added it now.
Thank you :)
The 'e' is explained in the Tips & Notes for the "Pronouns" unit:
Can you be more specific about the question that you have, please?