Here's the teams in the order of entry...

1. eastvanmungo - Pitching: Giants 1880's/2020's / Batting: Senators 1930's / Face: Joe Mauer*
2. stengelese - Pitching: Braves 1990's / Batting: Red Sox 2000's / Face: Pedro Martinez
3. fatguyrd - Pitching: Astros 2010's / Batting: Giants 1930's / Face: Buster Posey
4. 0soup4u - Pitching: White Sox 1900's / Batting: Dodgers 1940's / Face: Eddie Cicotte
5. mkohan - Pitching: Dodgers 1970's / Batting: Twins 1970's / Face: Sandy Koufax*
6. fatboydad54 - Pitching: Athletics 1970's / Batting: Yankees 1960's / Face: Mark McGuire
7. MAZZILLI16 - Pitching: White Sox 1940's / Batting: Blue Jays 1980's / Face: Frank Thomas
8. gilh14 - Pitching: Orioles 1960's / Batting: Dodgers 1950's / Face: Don Sutton
9. tensaver716: Pitching: Cubs 1940's / Batting: Phillies 1950's / Face: Jimmie Wilson*
10. spinaldog - Pitching: Athletics 1980's / Batting: Braves 2000's / Face: Rickey Henderson
11. DougDoty - Pitching: Giants 1900's / Batting: Braves 1960's / Face: Fred Toney
12. farleyfustle - Pitching: Padres 1970's / Batting: Cardinals 1970's / Face: Trevor Hoffman
13. finn2030 - Pitching: Highlanders 1900's / Batting: Athletics 1910's / Face: Marcus Semien
14. tensaver716 - Pitching: Doves 1900's / Batting: Rangers 1990's / Face: Big Jeff Pfeffer*
15. mkohan - Pitching: Browns/Cardinals 1880's/2020's / Batting: Beaneaters/Braves 1880's/2020's / Face: Ripper Collins*
16. gwhouse - Pitching: Yankees 1970's / Batting: Bees 1940's / Face: Joe DiMaggio*
17. Bradsher - Pitching: Jays 2000's / Batting: Nationals 2010's / Face: Steve Rogers
18. ChinMusic22 - Pitching: Cardinals: 1950's / Indians: 1940's / Face: Albert Pujols
19. gwhouse - Pitching: Tigers 2010's / Batting: Tigers 1960's / Face: Charlie Gehringer*
20. eastvanmungo - Pitching: Reds 1940's / Batting: Phillies 1890's / Face: Bill Henry
21. joerat1 - Pitching: Yankees 1960's / Batting: Reds 1950's / Face: Russ Ford
22. littlereb - Pitching: Dodgers 2010's / Batting: Giants 2000's / Face: Tim Keefe
23. adsmith182 - Pitching: Phillies 1900's / Batting: Mariners 2000's / Face: Pete Alexander
24. dhomard - Pitching: Diamondbacks 2000's / Batting: Naps 1910's / Face: Jim Thome

*owners with 2 teams

Here's the randomization sequence...

bheid408

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Here is your sequence:

8 22 16 24 13 18 14 23 20 10 21 11 2 7 6 19 9 3 12 5 17 1 4 15

Timestamp: 2023-06-27 22:59:57 UTC

6/27/2023 7:00 PM

So here's the initial alignment, not considering owners with multiple teams

NL East

1. gilh14 - Orioles/Dodgers
2. littlereb - Dodgers/Giants
3. gwhouse -Yankees/Bees (team 1)
4. dhomard - Diamondbacks/Naps

NL Central

1. finn2030 - Highlanders/Athletics
2. ChinMusic22 - Cardinals/Indians
3. tensaver716 - Doves/Rangers (team 2)
4. adsmith182 - Phillies/Mariners

NL West

1. eastvanmungo - Red/Phillies (team 2)
2. spinaldog - Athletics/Braves
3. joerat1 - Yankees/Reds
4. DougDoty - Giants/Braves

AL East

1. stengelese - Braves/Red Sox
2. MAZZILLI16 - White Sox/Blue Jays
3. fatboydad54 - Athletics/Yankees
4. gwhouse - Tigers/Tigers (team 2)

AL Central

1. tensaver716 - Cubs/Phillies (team 1)
2. fatguyrd - Astros/Giants
3. farleyfustle - Padres/Cardinals
4. mkohan - Dodgers/Twins (team 1)

AL West

1. Bradsher - Jays/Nationals
2. eastvanmungo - Giants/Senators (team 1)
3. 0soup4u - White Sox/Dodgers
4. mkohan - Browns/Beaneaters (team 2)

So, only mkohan has two teams in the same league... which means the second team he entered (Browns/Beaneaters) will move from the #4 position in the AL West to the #4 position in the NL West and DougDoty's Braves/Giants will move from the #4 position in the NL West to the #4 postion in the AL West. Making the final alignment look like so...

NL East

1. gilh14 - Orioles/Dodgers
2. littlereb - Dodgers/Giants
3. gwhouse -Yankees/Bees (team 1)
4. dhomard - Diamondbacks/Naps

NL Central

1. finn2030 - Highlanders/Athletics
2. ChinMusic22 - Cardinals/Indians
3. tensaver716 - Doves/Rangers (team 2)
4. adsmith182 - Phillies/Mariners

NL West

1. eastvanmungo - Red/Phillies (team 2)
2. spinaldog - Athletics/Braves
3. joerat1 - Yankees/Reds
4. mkohan - Browns/Beaneaters (team 2)

AL East

1. stengelese - Braves/Red Sox
2. MAZZILLI16 - White Sox/Blue Jays
3. fatboydad54 - Athletics/Yankees
4. gwhouse - Tigers/Tigers (team 2)

AL Central

1. tensaver716 - Cubs/Phillies (team 1)
2. fatguyrd - Astros/Giants
3. farleyfustle - Padres/Cardinals
4. mkohan - Dodgers/Twins (team 1)

AL West

1. Bradsher - Jays/Nationals
2. eastvanmungo - Giants/Senators (team 1)
3. 0soup4u - White Sox/Dodgers
4. DougDoty - Giants/Braves