hmm interesting!
I'll say first up that I am very much still in the beginner camp with fly fishing, but "balance" is something I know a fair bit about, and I trust Jims opinion.
as I read horses comment I was thinking "oh no not again!"
The idea that the "balance" of something can be demonstrated by where it balances along it's length is at best too simplistic, at worst completely misleading.
The problem is the word has 2 different meanings
balance - literally the point on which it balances
"balance" - the partly subjective feeling of how easy or comfortable it is to move the object around in the way it was designed to be used.
The 2 aren't closely related.
I make wooden swords and restore antique ones - a field in which "balance" is extremely important.
you can have 2 swords with the same point of balance that have completely different "balance", or 2 that feel similarly "balanced" with completely different points of balance!
"balance" is down to things like distribution of weight and centre of rotation.
I have seen people talking about the "balance" of swords by comparing the pob and also a guy selling an open razor showing how well "balanced" it was with a pic of it balanced on his finger. So the misunderstanding is fairly common.
a bit off topic there and not actually much help with your problem

but don't worry too much where the pob on your rod is, is what I was getting at