First, it's usually easier to derive the definitions by direct manipulation in combinatory form:
h f g x y z = f x (g y z)
= B(fx)(gy)z -- B rule
= B(B(fx))gyz -- B rule
h f g x = B(B(fx))g -- eta-contraction
= BBB(fx)g -- B rule
= B(BBB)fxg -- B rule
= C(B(BBB)f)gx -- C rule
h f = C(B(BBB)f) -- eta-contraction
= BC(B(BBB))f -- B rule
h = BC(B(BBB)) -- eta-contraction
-- = B(B(CB(CB))(CB))(BB) -- your expression
The types are the same, though my expression is shorter. Can this serve as a counterexample to whether the combinatory form should somehow follow the given definition? There is considerable freedom in how the rules are applied, so widely different forms can be derived. I don't think much insight can be arrived at from a given combinatory expression.
If anything, the combinators that appear in the final translation are more representative of the derivation steps taken, and those can be chosen freely among those that fit, at any given point.
For example, the following step is commonly taken in deriving your expression, evidently:
g(fx) = Bgfx = CBfgx
B (B (CB(CB)) (CB)) (BB) f g x y z
= B (CB(CB)) (CB) (BB f) g x y z
= CB (CB) (CB (BB f)) g x y z -- and here
= CB (BB f) (CB g) x y z -- here
= CB g (BB f x) y z -- here
= BB f x (g y) z
= B (f x) (g y) z
= f x (g y z)
But if you prioritize your rules application and make it deterministic, you should always arrive at the same result -- which will depend on the order in which you apply the rules.