If I understand correctly then I do have an algorithm that will attempt to solve this, but unfortunately it can't find perfect solutions. For the 12 team division it gives:
(B J) (A G) (E K)
(F L) (C H) (D I)
(B L) (J K) (E G)
(F H) (C D) (A I)
------------------
(I K) (G H) (B D)
(E J) (A F) (C L)
(D H) (B K) (G I)
(C E) (F J) (A L)
------------------
(H K) (A B) (F I)
(D E) (J L) (C G)
(A K) (H I) (B F)
(D G) (E L) (C J)
------------------
(A C) (D L) (B H)
(F K) (E I) (G J)
(A D) (B C) (H L)
(I J) (G K) (E F)
------------------
(F G) (D J) (A H)
(C I) (B E) (K L)
(B G) (D F) (H J)
(A E) (I L) (C K)
------------------
(B I) (C F) (D K)
(G L) (E H) (A J)
Above there are two times where a team has to play back-to-back matches. L in week 1, and B in week 5.
For 16 teams it gives:
(L O) (I M) (F G) (B E)
(C H) (A K) (N P) (D J)
(B I) (E O) (D L) (G M)
(F K) (J P) (A H) (C N)
------------------------
(H I) (G N) (B J) (C O)
(E L) (F P) (K M) (A D)
(I N) (C J) (H O) (B G)
(A M) (K L) (E P) (D F)
------------------------
(D E) (C F) (B O) (M N)
(A P) (I J) (H L) (G K)
(E F) (C D) (B N) (M O)
(A J) (G P) (H K) (I L)
------------------------
(D P) (B H) (E I) (F M)
(G J) (A O) (L N) (C K)
(F H) (B D) (M P) (I O)
(C G) (E K) (J N) (A L)
------------------------
(E J) (F O) (D G) (H N)
(B K) (L M) (A C) (I P)
(G O) (H J) (F I) (E N)
(C M) (A B) (D K) (L P)
------------------------
(N O) (G I) (F L) (J K)
(D M) (H P) (B C) (A E)
(I K) (F N) (A G) (J L)
(B M) (D O) (C P) (E H)
------------------------
(A F) (B L) (E G) (C I)
(O P) (K N) (J M) (D H)
(G L) (C E) (A I) (B F)
(D N) (H M) (J O) (K P)
------------------------
(B P) (D I) (E M) (F J)
(C L) (A N) (K O) (G H)
Here there 4 back-to-back matches. D in week 1, O in week 4, I in week 5, and A in week 6.
Is that workable?
I am using a computer algorithm that examines many different schedules and picks the best one, the schedules are not generated totally at random, rather it tries to find schedules similar to others that have good properties.
I have just left the 12 team problem running for a couple of hours and it has found a slightly better solution with only one inconsistency.
(E K) (I J) (A B)
(G L) (D F) (C H)
(B I) (J K) (A E)
(F L) (D H) (C G)
------------------
(D L) (E H) (G I)
(C J) (A F) (B K)
(D G) (E L) (H I)
(B C) (A K) (F J)
------------------
(G H) (F I) (C K)
(A L) (B J) (D E)
(F H) (C I) (K L)
(E J) (B G) (A D)
------------------
(I K) (A J) (H L)
(C F) (E G) (B D)
(A I) (H K) (J L)
(B E) (C D) (F G)
------------------
(D J) (I L) (B H)
(A G) (C E) (F K)
(H J) (B L) (D I)
(A C) (G K) (E F)
------------------
(B F) (A H) (E I)
(D K) (C L) (G J)
Team L is back-to-back in week 3, while G gets the 1 hour break.