B67 regular here. (not "S" for "short")
Levelled the noses on both of mine. The cantle plate ends up looking a bit higher, but don't let that fool you. Brooks are meant to start with a level nose rather than levelling the whole saddle.
I agree with the other posts, if your current saddle is so narrow that you only have one perch and tend to come off it and it feels very hard; it kinda sounds like you might be perching on the cantle plate rather than putting your sit bones onto the suspended leather forward and medial of the cantle plate. (where the saddle is narrower)
Maybe see if you can try a wider Brooks borrowed from a friend or bike shop, so you can compare?
(whether you want a "short" or not is up to you. I prefer long noses just because I like to control the bike with my legs and have room to scoot around during long rides.)
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