You need to have a technical lead for for every five or six offshore engineers. These leads act as the bridge between the offshore and US teams and must, therefore, work a shift that overlaps both teams. They must be senior enough to be able to track the work done by both teams without becoming a burden to either team. They must also understand the implications of daily decisions, and be able to clarify any misunderstandings before they create a crisis.
For a nearshore or onshore location, this ratio can be much higher, or even eliminated altogether, lowering the overhead cost. That is because the proximity (i.e., two time zones at most) allows the local and remote teams to communicate throughout the day, as needed (e.g., using IM or voice). This casual style of communication just about eliminates the need to hold formal meetings at off hours.
As with the Engagement Manager, find people who have had experience working with a remote team, preferably somebody who understands the cultural differences between your team and the remote team.
Besides the appropriate technical qualifications, the ideal candidates should better than average people skills.
As mentioned above, the Tech Leads must be willing and able to work an appropriate shift that overlaps sufficiently with the US-based team and the remote team.
They must be willing to travel to the offshore location if necessary.