If you follow the schedules link above, then click on Balanced and finally dial up 20 players - then I think this will give you most of what you want. Assign the first six matches to be early games on pits one to six, and the last four matches as the late games. For the late games perhaps you should use only the 'best' four pits , then teams will play at least three times and at most four times on each of the best pits. A team will either, play 11 early games and 8 late games, or play 12 early games and 7 late games.
My
Excel file here (version 4.3) will give you a similar schedule.