I think you may already have a good solution, so I would be interested to know what you have done to get to the schedule in the Excel file. My insitinct is to try to make 8 weeks where all the foursomes are of the 'Mixed Type' where there are two players from each of two groups, and then have a final round (or two rounds) where the foursomes are of the 'Group Type', with foursomes corresponding to group membership. I can then think of two strategies for searching for a solution:
(1) There are exactly 48 possible pairs of two players where the two players come from different groups. You could try rearranging these pairs to form an 8 week schedule. Of course this automatically gives balance for players in a cart together. I have not tried this option.
(2) I noted that there are exactly 1728 possible ways to assign play for a week, where all 3 foursomes are of the Mixed Type. So I looked for ways of selecting 8 weeks from 1728 to give a schedule. This was not totally successful, and the method is only finding schedules like the one below, where you would need to add two Group Type rounds, both with 2 matches per player. This gives 4x replication of the within division matches.
The schedule below uses numbers rather than letters, so A=1, B=2, C=3, etc., and it is presented with the same layout as your Excel file, where weeks are rows, and pairs of adjacent columns are carts.
1 8 3 5 2 12 4 10 6 11 7 9
1 7 2 8 3 9 4 11 5 12 6 10
1 5 3 6 2 11 4 9 7 10 8 12
1 6 4 7 2 10 3 11 5 9 8 12
2 7 4 5 1 9 3 10 6 12 8 11
2 7 3 6 1 10 4 12 5 11 8 9
3 8 4 6 1 12 2 9 5 10 7 11
2 5 4 8 1 12 3 11 6 9 7 10
1 3 2 4 5 8 6 7 9 11 10 12
1 3 2 4 5 8 6 7 9 11 10 12