Bozak had 26 straight in March of 2015! He won his last 10 draws in a game (coincidentally all in the 3rd period), then opened the next game 16/16. That took him all the way to OT, where he lost his opening draw. So exactly 4 periods of 26/26.
I looked through the best faceoff games since 07/08 (since that's when you can actually find records of the sequencing of faceoffs) where a player didn't lose a draw in a game and won at least 10 (29 occurrences of that happening, including Bergeron), then I looked at games where a player won at least 15 draws and only lost 1 (12 occurrences). I went through the perfect game ones first, where Helm's 18 was the best mark, then started on the 1-loss games. Admittedly I didn't count exactly after seeing Bozak's if it wasn't going to be close, but Bergeron and Bozak are well ahead of the others.
Another highlight:
- Darren Helm won 18 straight in April of 2014, across a crazy 4-game period. He won his last draw of a game, then went 6/6 next game, 10/10 the game after that, then won his first draw of the next game.
Digging back older than that:
- Dave Scatchard went 19/19 in a January game in 2000, but I cannot find any sequencing of faceoffs in other games surrounding it. I just know that he went 9/22 the game before and 5/13 the game after, so it's probably unlikely he had 25 straight.
- Curtis Brown in 2000 also went 19/19 on the first game of the 2000/01 season. The next game he went 12/23, and on the last game of the 1999/00 season he went 8/15. A bit more likely but who knows.