I have found the following schedule by computer search and I think it will work for your soccer league.
w1 early (G L) (H I) (B C)
w1 late (E F) (J K) (A D)
w2 early (B F) (G I) (A E)
w2 late (C D) (H J) (K L)
w3 early (I K) (A F) (G H)
w3 late (B D) (C E) (J L)
w4 early (D E) (I L) (A B)
w4 late (G J) (H K) (C F)
w5 early (H L) (G K) (D F)
w5 late (I J) (B E) (A C)
w6 early (B C) (J K) (D E)
w6 late (G H) (A F) (I L)
w7 early (K L) (E F) (G J)
w7 late (A C) (B D) (H I)
w8 early (A B) (C E) (I J)
w8 late (D F) (H L) (G K)
w9 early (J L) (C D) (H K)
w9 late (A E) (B F) (G I)
w10 early (H J) (A D) (C F)
w10 late (I K) (G L) (B E)
For weeks 11 to 12 use the same schedule but swap the teams around as follows:
AD
BE
CF
GJ
HI
KL
Here AD means that the team that was assigned to A in rounds 1 to 10 is assigned to D in weeks 11 to 20, and the team that was D becomes A.
If you do all that, then you should have a schedule with the following properties. Each team plays:
- Once per week
- 10 early games & 10 late games
- 6 or 7 times on each field
- Each other team in the same group 4 times (exactly once in each block of 5 weeks)
- The schedule should also have the alternating pattern you asked for
With the current problems on the message board, I am not sure if you will be able to add replies in this thread. If you can't then send me a email by clicking on my name.