Instead of doing the CBSJ, you can do a Fixed Camera Glide into a Midair Glidewalk. Right before grabbing the ledge, make sure to hold Y, then upon grabbing the ledge, press A once and then hold A and hold down and you Glidewalk along the wall. Easy.
This method was not found by me, but GamePro. He used it in this run that's 3 years old since this video, but people should be using this alternative since it's not bad at all: https://www.twitch.tv/videos/49321722?t=1h18m54s
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