= Solution
Keeping both <gradient> coefficients fixed requires $z^2=Bb^2=Bc^4$. Hence
$$
c=b^{1/2},\qquad B=b^{(d+1)/2},\qquad z=b^{(d+5)/4}.
$$
Equivalently the real-space field normalization is $z_x=z/B=b^{(3-d)/4}$. The transformed thermal and source couplings are
$$
\boxed{t'=b^2t,\qquad h'=b^{(d+5)/4}h,\qquad y_t=2,\quad y_h=(d+5)/4.}
$$
This is the <Gaussian fixed point> at $t=h=0$, with anisotropic effective volume exponent $D_{\rm eff}=(d+1)/2$. The stiffnesses remain positive parameters labeling the normalization of coordinates and fields. A strictly positive $t$ is a relevant perturbation away from the <renormalization-group fixed point>, not itself a critical <renormalization-group fixed point>.
The two <correlation lengths> also follow directly by balancing the kernel: $Kq_\parallel^2\sim t$ gives $\xi_\parallel\sim(K/t)^{1/2}$, while $Lq_\perp^4\sim t$ gives $\xi_\perp\sim(L/t)^{1/4}$. Their different exponents are consistent with the required anisotropic scaling. An omitted scalar quartic interaction has scaling <eigenvalue> $4-D_{\rm eff}=(7-d)/2$, so the quadratic <renormalization-group fixed point> alone does not establish the interacting smectic's critical behavior below physical dimension seven.
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