Have successfully created the Dist. AVG across the data centers.
There's been a change in architecture from my initial description; instead of multiple instances, we have multiple AVG. The production environment at Data Center 1 (DC1) has two AVGs configured with two listeners. That is, NODE_1 is primary for AVG_1 with LIST_1, and NODE_2 is primary for AVG_2 with LIST_2. DR requirements specify that the same environment be created at DC2 and that the databases sync across DCs.
In the DR environment, we created a 2-node AlwaysOn AG and configured two AVGs (AVG_3 and AVG_4). Then we created two distributed availability groups connecting AVG_1 to AVG_3 and AVG_2 to AVG_4.