Now that I figured out how to make tables, I'm going to keep using this new-found power and show the representation so far of each dynasty (and modern quasi-dynasties):
Rank | Player | Team | Cups in timeframe
51|King Clancy|1919-27 Senators|2
53|Clint Benedict|1919-27 Senators|4
64|Sprague Cleghorn|1919-27 Senators|2
67|Cy Denneny|1919-27 Senators|4
??|Frank Nighbor|1919-27 Senators|4
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38|Syl Apps|1947-51 Maple Leafs|2
57|Max Bentley|1947-51 Maple Leafs|2
59|Turk Broda|1947-51 Maple Leafs|4
70|Ted Kennedy|1947-51 Maple Leafs|4
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3|Gordie Howe|1949-55 Red Wings|4
16|Red Kelly|1949-55 Red Wings|4
24|Terry Sawchuk|1949-55 Red Wings|3
30|Ted Lindsay|1949-55 Red Wings|4
??|Sid Abel|1949-55 Red Wings|2
??|Alex Delvecchio|1949-55 Red Wings|3
??|Black Jack Stewart|1949-55 Red Wings|1
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6|Doug Harvey|1956-60 Canadiens|5
7|Jean Beliveau|1956-60 Canadiens|5
9|Maurice Richard|1956-60 Canadiens|5
13|Jacques Plante|1956-60 Canadiens|5
43|Bernard Geoffrion|1956-60 Canadiens|5
55|Henri Richard|1956-60 Canadiens|5
63|Dickie Moore|1956-60 Canadiens|5
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16|Red Kelly|1961-67 Maple Leafs|4
49|Frank Mahovlich|1961-67 Maple Leafs|4
56|Andy Bathgate|1961-67 Maple Leafs|1
62|Tim Horton|1961-67 Maple Leafs|4
??|Johnny Bower|1961-67 Maple Leafs|4
??|Dave Keon|1961-67 Maple Leafs|4
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7|Jean Beliveau|1964-69 Canadiens|4
55| Henri Richard|1964-69 Canadiens|4
??|Serge Savard|1964-69 Canadiens|1
??|Yvan Cournoyer|1964-69 Canadiens|4
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19|Guy Lafleur|1975-79 Canadiens|4
31|Larry Robinson|1975-79 Canadiens|4
39|Ken Dryden|1975-79 Canadiens|4
??|Serge Savard|1975-79 Canadiens|4
??|Yvan Cournoyer|1975-79 Canadiens|4
??|Bob Gainey|1975-79 Canadiens|4
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18|Denis Potvin|1980-83 Islanders|4
26|Bryan Trottier|1980-83 Islanders|4
29|Mike Bossy|1980-83 Islanders|4
??|Billy Smith|1980-83 Islanders|4
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1|Wayne Gretzky|1984-90 Oilers|4
22|Mark Messier|1984-90 Oilers|5
46|Paul Coffey|1984-90 Oilers|3
69|Jari Kurri|1984-90 Oilers|5
??|Grant Fuhr|1984-90 Oilers|5
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4|Mario Lemieux|1991-92 Penguins|2
23|Jaromir Jagr|1991-92 Penguins|2
26|Bryan Trottier|1991-92 Penguins|2
46|Paul Coffey|1991-92 Penguins|1
??|Ron Francis|1991-92 Penguins|2
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37|Martin Brodeur|1995-03 Devils|3
??|Scott Stevens|1995-03 Devils|3
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10|Raymond Bourque|1996-01 Avalanche|1
14|Patrick Roy|1996-01 Avalanche|2
32|Joe Sakic|1996-01 Avalanche|2
65|Peter Forsberg|1996-01 Avalanche|2
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12|Dominik Hasek|1997-02 Red Wings|1
17|Nicklas Lidstrom|1997-02 Red Wings|3
33|Slava Fetisov|1997-02 Red Wings|2
36|Steve Yzerman|1997-02 Red Wings|3
41|Chris Chelios|1997-02 Red Wings|1
??|Brett Hull|1997-02 Red Wings|1
??|Sergei Fedorov|1997-02 Red Wings|3
I included every player who made the list last year or who I think has a chance to make it based on who I see voters talking about.
As noted earlier, the 60s Canadiens and dead puck era Devils are notable for their lack of star power compared to their team success. This is enough for me to give the undisputed leaders on the teams (Beliveau and Stevens) a bit of a boost. The undisputed leader of a team getting his teammates to buy into a team concept that leads to multiple championships absolutely makes him a better hockey player in my opinion.