Yes, this is actually what I meant by "vertical teams guiding the reform".

A large urban district can have a very interesting culture. (I worked in Los Angeles Unified for 20 years.) One possible way to start at the top is to determine who/what influences the "top". In many cases the voice of the local professional science or mathematics community, the chamber of commerce, business or industry officials who are "large" players in the community can be helpful.
They are more helpful if these players have been part of the vertical team. It is always important to have someone with decision-making authority from the central office on the vertical team.
Also have one of the superintendents from one of the other collaborating district's meet with the large urban. Or have a joint meeting of just the superintendents. We seem to feel comfortable is asking what we don't know with our peer group.

The key issue is usually focused on something like: " How will this reform provide our ...... with the ability to do ........ better."

Also, as a peer to people on the top (ha!) I would always be glad to make a call.