[pilun]

It's hard to achieve symmetry with balanced hands. Too many 4432s that want to end at the same point, likewise 5332s. Doh!
There is more to be gained by following Fibonacci to lower the endpoint.
We've decided to stick with unlimited balanced hand responses but they need compacting to give opener the space for a safe strength ask.
Previously we had 3S last shape with 3H non-zoom, which was not great.

These are our GF responses:
1H = spades, not flat
1S = hearts, not spades, not flat
1N = 6+Ds or 5+4 minors, no major
2C = flat with a major
2D = balanced, no major
2H = 3-suited, both minors
2S+ = 6+ clubs

There are alternatives, such as 1S = balanced or red suits. We've preferred to avoid multi-meaning bids.

Anyway, back to 2C which shows 12 hand shapes, a very good Fibonacci split.
One natural spread is S+m, H+m, both, square. That's 4+4+2+2. No good.

With 4 at the end, 1-1-1-1 is just as good as 2-1-1 so the aim is 5-3-1-1-1-1
Fine if we move 4-3-3-3 to 2H, then take a hand from H+m to get

2H = spades, not hearts (5)
2S = hearts & a minor (3) drop one
2N = 4-4-2-3
3C = 4-4-3-2 (better not to bid 2NT with both of these to avoid wrong-siding)
3D = 2-4-4-3, the swapped out shape
3H+ = 3-4-3-3

In all streams, the zooming shape is 3H, which is perfect (3H = 5 or 6, 3S = 7, 3NT = 8, 4C = 9, resurrection strength)
3D non-zoom is okay, since opener still gets a choice of two asks (SPs or Kontrols for us). KK uses +1 as a weak kontrol ask.

2H = S ________________________
2S = H _____________ ..........|
2N = 4-4-2-3 ......| ........S & D _________
3C = 4-4-3-2 ... 3-4-4-2 ... 4-2-3-4 .......|
3D = 2-4-4-3 ... 2-4-3-4 ... 4-3-2-4 ... 4-2-4-3
3H+ = 3-4-3-3 .. 3-4-2-4 ... 4-3-3-3 ... 4-3-4-2

Not such a memory strain:
"spades, not hearts - hearts & a minor - both high - both low - reds high - square hearts"

The 10 balanced shapes with no major are problematic. 10 is a bad Fibonacci number. We dropped the 4-4 minor hands to get

2D - 2H
2S = 5 diamonds
2N = square
3C = 2-3-3-5
3D = 3-2-3-5
3H+ = 3-3-2-5

This is a perfect Fibonacci structure, three streams ending at 3H zooming. It's also symmetric looking.
What about 4-4 minors?

We put them in 2H, which simply becomes "both minors" so

2H - 2S
2N = 4 spades
3C = balanced (2 shapes)
3D = 1-4-4-4
3H = 0-4-4-5
3S = 0-4-5-4
3N = 0-5-4-4

The 3-suiters are pleasantly symmetric, with 3C a neat pivot. (With 5440s, we resolve "canape first")



One problem with unlimited balanced hands is the need for opener to go to (near) resolution in case responder has a big hand.
We can't really have 1C - 2D - 3NT. Have to ask once, unless 3NT is VERY specific.
With shape half-known, we use Step +1 as "Forget the residue, show SPs."

[awm]

It seems like with 5M-(332) you are responding 1M and then resolving at 2♠+, whereas you use 2♠+ to show 6+m one-suited, so you're sort of gaining a step on the one-suited minor hands. If you put 5m-(332) into 1NT (diamonds) or 2♠+ (clubs) then the resolution becomes more symmetric and you gain a step on the balanced hands (which now exclude 5m-(332)). Since you're playing GF responses and relay I don't think there's a big advantage to treating 5m-(332) as balanced.