Caracol flow-polytope volume conjecture for three initial parameters

Let $\textup{Car}_{n+1}$ be the Caracol graph on $n+1$ vertices, and let $\mathcal{F}_{\textup{Car}_{n+1}}(a,b,c,\ldots,c)$ denote its flow polytope with the indicated net flow vector. Caracol volume conjecture. For $n\geq2$ and positive integers $a$, $b$, and $c$,

$$\operatorname{vol}\mathcal{F}_{\textup{Car}_{n+1}}(a,b,c,\ldots,c)=C_{n-2}\cdot a^{n-2}(a+(n-1)b)(a+b+(n-2)c)^{n-3}.$$

The formula is verified in the source up to $n=8$ and would imply the preceding theorem when $b=c$.