We compute a multi-test census of small-height pseudoprimality liars, recording foreach odd composite $n$ the interval-local Miller--Rabin and Euler--Jacobi spectra$\sigmamr(n;A),\sigmaej(n;A)$, the strong-Lucas grid spectrum $\sigmasl(n;A)$ over$P\in[1,A]$, $Q\in\{\pm1\}$, and Baillie--PSW, Frobenius and extra-strong Lucasindicators. A CUDA backend (RTX~5090), verified bit-for-bit against a CPUreference, reaches $N=10^{11}$ at $A=1000$ in $68.8$ hours; it reproduces the priorrecord-holder $3215031751$, the OEIS base-2 strong-pseudoprime counts ($8607$ below$10^{11}$), and the empty Baillie--PSW survivor set below $10^{11}$. The strong-Lucas-extremal composites are essentially disjoint from the MR-extremalones (all carry $\sigmamr=0$; at $10^{11}$ the top-$100$ sets share one composite),and are dominated by the semiprime family $n=p(2p+3)$. We prove a local CRTcriterion for strong-Lucas pseudoprimality in terms of the rank of apparition (theLucas analogue of the corrected Miller--Rabin local-order criterion, independentlyverified computationally). It identifies $q=2p+3$ as the coefficient-$2$ affinefamily aligning the nonsplit $p+1$ rank with the split $q-1$ rank, sharpens in themixed character regime to an exact criterion (strong-Lucas $\iff v_2(\rho_p)=v_2(\rho_q)$), and exhibits $\sigmasl(n;A)$ as a small-height sum offixed-discriminant slices of Arnault's strong-Lucas parameter counts. The residue clustering $n\equiv77\pmod{100}$ among the strong-Lucas extremes is aselection effect of $\sigmasl$ via the character $\left(\tfrac5n\right)$ and the$p\bmod4$ structure, not a prime-pair density artifact. We give the unconditionalmechanism and a conditional average-order dominance theorem, and isolate the exactanalytic obstruction, a Bateman--Horn and $2$-adic rank-equidistributioninput, to a ranked-tail asymptotic; asymptotic claims beyond the enumerated rangeare explicitly avoided.