= Solution
Write $K=k_1+k_2+k_3>0$ and $C=\epsilon+1-c_s^2$. The <inflationary scalar Fourier mode> has real late-time value $A_k=H/\sqrt{4\epsilon M_{\rm Pl}^2c_sk^3}$ and $u_k'^*(\tau)=A_kc_s^2k^2\tau e^{ikc_s\tau}$. Thus the time integrand, before the factor $-2i$, is
$$
\frac{M_{\rm Pl}^2\epsilon C}{H^2c_s^2\tau}\prod_{r=1}^3u_{k_r}(0)u_{k_r}'{}^*(\tau)=\frac{H^4c_sC}{64\epsilon^2M_{\rm Pl}^4k_1k_2k_3}\tau^2e^{ic_sK\tau}.
$$
The <Bunch-Davies vacuum> prescription supplies damping in the past. Equivalently, use a positive regulator $d$ and then take the limit:
$$
\int_{-\infty}^0\tau^2e^{(d+ic_sK)\tau}\,d\tau=\frac2{(d+ic_sK)^3}\longrightarrow\frac{2i}{c_s^3K^3}\qquad(d\downarrow0).
$$
The real part of $-2i$ times this integral is $4/(c_s^3K^3)$. Including the six <Wick contractions> yields the <cubic time-derivative curvature bispectrum>
$$
\boxed{B(k_1,k_2,k_3)=\frac{3H^4(\epsilon+1-c_s^2)}{8\epsilon^2M_{\rm Pl}^4c_s^2k_1k_2k_3(k_1+k_2+k_3)^3}.}
$$
The resulting <primordial bispectrum> is a <homogeneous function> of degree $-6$ in the wavenumbers, as expected for scale-independent background parameters.
The printed limit $c_s\ll0$ is not a physical sound-speed limit for these modes. The normalization and positive-frequency choice assume $c_s>0$; a negative value is outside the positive sound-speed convention used by these modes. The likely intended limit is \b[$0<c_s\ll1$], which is analyzed explicitly here rather than silently substituted for the PDF.
To compare <primordial non-Gaussianity>, normalize by the <power spectrum>, not only by the raw three-point amplitude. Here
$$
P_\zeta(k)=\frac{H^2}{4\epsilon M_{\rm Pl}^2c_sk^3},\qquad \Delta_\zeta^2=\frac{k^3P_\zeta(k)}{2\pi^2}=\frac{H^2}{8\pi^2\epsilon M_{\rm Pl}^2c_s}.
$$
At an <equilateral bispectrum configuration>, the exact normalized amplitude is
$$
\boxed{\frac{B(k,k,k)}{P_\zeta(k)^2}=\frac29(\epsilon+1-c_s^2).}
$$
Thus $c_s\to1$ gives an amplitude of order $\epsilon$, consistent with weak non-Gaussianity in <single-field slow-roll inflation>. For $0<c_s\ll1$, this vertex gives an amplitude of order one, enhanced relative to the slow-roll limit but not diverging as $c_s^{-2}$ after power-spectrum normalization. At fixed $H,\epsilon,M_{\rm Pl}$ the raw bispectrum does scale as $c_s^{-2}$, but $P_\zeta^2$ has the same scaling. The often-quoted larger small-sound-speed amplitudes of more general inflationary actions require their actual interaction coefficients and other vertices; they do not follow from the lone supplied vertex. These conclusions concern its tree contribution within the stated weak-perturbation approximation.
The <bispectrum shape function> is
$$
S\propto\frac{k_1k_2k_3}{(k_1+k_2+k_3)^3}.
$$
At fixed perimeter, the <arithmetic-geometric mean inequality> bounds this by $1/27$, attained only at an <equilateral bispectrum configuration>. In a <squeezed bispectrum configuration> with $k_1=q\ll k_2\simeq k_3=k$, it behaves as $q/(8k)\to0$. At a <flattened bispectrum configuration> $(k,k,2k)$ it is finite, $1/32$, with no boundary singularity. Thus \b[the shape prefers equilateral triangles and suppresses squeezed triangles], with a broad finite flattened contribution. This is a shape preference, not a complete signal-to-noise calculation: actual observational weighting also depends on <cosmological transfer functions>, <covariance> and accessible triangles. If $C=0$, this vertex produces no bispectrum at any configuration; if $C<0$, the signed shape reverses while its absolute triangle preference is unchanged.
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