Now that we've established a routine for the drafts, I mapped out approximate dates for this tournament. Assuming there are no lengthy delays, here is what I came up with for a general timeline.

Round 1

League 1
Draft: July 10-20
League: July 23 - September 14
.
League 2
Draft: July 21-29
League: July 31 - September 22
.
League 3
Draft: July 30 - August 7 (Draft ended August 6)
League: August 9 - October 1
.
League 4
Draft: August 8-16 (Draft ended August 14)
League: August 18 - October 10
.
League 5
Draft: August 17-25 (Draft ended August 22)
League: August 27 - October 19
.
League 6
Draft: August 26 - September 3 (Draft ended August 31)
League: September 5 - October 28
.
League 7
Draft: September 4-12 (Draft ended September 10)
League: September 14 - November 6
.
League 8
Draft: September 13-21 (Draft ended September 16)
League: September 23 - November 15
.
League 9
Draft: September 22-30 (Draft ended October 6)
League: October 2 - November 24
.
League 10
Draft: October 1-9 (Draft ended October 12)
League: October 11 - December 3
.
League 11
Draft: October 10-18 (Draft ended October 21)
League: October 20 - December 12
.
League 12
Draft: October 19-27 (Draft ended October 29)
League: October 29 - December 21

Round 2

League 1
Mini-drafts: September 15 & 23 (Mini-drafts ended September 15 & 23)
League: September 26 - November 18
.
League 2
Mini-drafts: October 2 & 11 (Mini-drafts ended October 3 & 10)
League: October 14 - December 6
.
League 3
Mini-drafts: October 20 & 29 (Mini-drafts ended October 18 & 27)
League: November 1 - December 24
.
League 4
Mini-drafts: November 7 & 16 (Mini-drafts ended November 5 & 13)
League: November 19 - January 11
.
League 5
Mini-drafts: November 25 & December 4 (Mini-drafts ended December 1 & 9)
League: December 7 - January 29
.
League 6
Mini-drafts: December 13 & 22 (Mini-drafts ended December 18 & 28)
League: December 25 - February 16

Round 3

League 1
Mini-drafts: December 7 (Mini-draft ended December 9)
League: December 10 - February 1
.
League 2
Mini-drafts: January 12
League: January 15 - March 9
.
League 3
Mini-drafts: February 17
League: February 20 - April 14

The final mini-drafts and Round 4 will begin in mid April.

FYI - it is possible for somebody to have more than 2 teams in the final round. First assume all 16 original members of league 1 play all 16 leagues. Then assume the extreme situation of the same 8 people advancing from each of the sixteeen leagues to round 2. Since round 4 consists of 24 teams, you need 12 unique owners to guarantee nobody has more than 2 teams. Even the non-extreme example of 9, 10 or 11 unique owners advancing to round 3 would result in somebody getting to play more than 2 teams in round 4.

Note the mini-drafts for round 3 only have one date, because going from 6 leagues to 3 leagues, we have to see who has more than 2 qualifying teams advancing before we can determine which teams officially advance. For example, League #1 from round 2 ends 18 days before League #2 (Nov 18 vs Dec 6). Since those two leagues feed into round 3, we have to wait to see the results of League #2, in order to determine the 16 advancing teams - then we would have the mini-drafts on Dec 7.