UPDATE:
We finally got the new neighborhood signature forms and went out this morning and gathered more than enough signatures in less than an hour. Neighbors we knew stopped neighbors we did not know who were walking along the street and had them sign. Very friendly reception and I had to promise only a few more cervezas (don't tell city hall that I offered bribes....

).
The last of the modifications to the place should be finished this weekend. I cleaned the grease trap (ugh, ugh, ugh) and it is about to be installed.
We are now ready to head to city hall. Just need to figure out which city hall to go to. jaja.
And then we get inspected by Ecologia and Civil Proteccion to make sure that our grease trap is working and that our fire extinguisher is ok, etc.
And then we wait and see what other things we have forgotten or did wrong, etc.
This process is a crash course in Mexican culture.
Sometimes, while doing this, we are scared to death, sometimes we are almost totally frustrated and sometimes we smile a lot.