If you modify the first round of the original schedule as I have illustrated above, then the net result is:
1 game less between set A and set B.
1 game less between set C and set D.
1 game more between set A and set D.
1 game more between set B and set C.
You need to make more swaps like this, any B set team for any D set team, within any of the first 4 rounds, until the balance of games between the various sets becomes more even. Within the last four rounds the swaps will be of a different type, swapping any C set team with any D set team which results in:
1 game less between set A and set C.
1 game less between set B and set D.
1 game more between set A and set D.
1 game more between set B and set C.
If you can make 5 swaps of the first kind and 5 swaps of the second kind, such that all the created games between AD and BC are different, then the schedule will have best possible balance for inter-set games.