Cut back the EVA and the grip tenon in 1/16" increments until it fits flush. Without a lathe it may be difficult to get a straight cut on the EVA. I've never had your case but often the butt cap is larger than the grip with CFX carbon fiber from Mud Hole.
I prefer tension on the sides of the spool with a flexible reverse tension device. I use 4 different wrappers at times and they all are set up that way. Don't know about better but that is how I learned a long time ago. Look at the CRB Core as an inexpensive basic but well designed hand wrapper.
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