Just went through the whole process, figured should share some tips:

Once you booked the ticket:

1. Call Delta to get the PNR for China Eastern. (was told by Delta agents that this info can only be obtained by calling)

2. Call China Eastern 1 (800) 200-5118 to select seat. The agents do not seem to be very familiar with airplane types and seat configuration so it would be a good idea to pull the seat map from delta.com by selecting the exact same flight's seat map, and have that in front of you.

Overall, it's a pain but it's easier than I thought.