Exceptional supersphere integration and logarithmic Pizzetti kernels

We study orthosymplectically invariant supersphere integration at the exceptional superdimensions $M=-2u$, where the harmonic Fischer structure becomes nonsemisimple and the Pizzetti pairing degenerates. For the meromorphically continued homogeneous inverse kernels we obtain the generating function \[
\mathscr G_\mu(\rho;x,y)
=\frac{\Gamma(\mu/2)}{2\pi^{\mu/2}}
\bigl(1+\rho\{x,y\}+\rho^2x^2y^2\bigr)^{-\mu/2}. \] At $\mu=-2u$, its Laurent expansion has a polynomial residue and a logarithmic finite part. We prove that these coefficients recover the complete degreewise duality structure on a fixed superspace with nonzero bosonic dimension. In degrees $k\le u$, the residue inverts a canonical renormalized pairing on $\mathcal P_k$. In the collision range $u<k\le2u$, the ordinary pairing has radical $(x^2)^{k-u}\mathcal P_{2u-k}$; the finite part reproduces the quotient, while the residue reproduces the radical after transport from the reflected degree. For $k\ge2u+1$, the finite part is the ordinary inverse kernel. We also establish the nondegenerate head--socle pairing on the generalized harmonic modules. As an application, we derive covariant right--left radial $q$-monogenic zonal symbols and identify precise degree-one obstructions to transferring scalar Pizzetti reproduction through a one-sided $q$-Fischer projection.