Is it possible to have a conditional dropdown based on a many to many relationship in a grandparent?

I believe that I understand your question and it can be done natively.  But you would need to contact me via the information in my profile for one on one assistance with this.  The solution is too complicated to post here.  Its not crazy complicated but does require updating a table of users to indicate which project they are Focussed on.  Then "lighting up" the building List for that Project and hence lighting up the Buildings for those who qualify for the Project to choose.