Saikia and Sarma's congruence conjectures for overcubic partition triples

Let $\overline{bt}(n)$ denote the number of overcubic partition triples of $n$.

Saikia and Sarma's conjecture. For $n,\alpha\geq 0$,

$$\overline{bt}(144n+42)\equiv 0\pmod{384},\qquad \overline{bt}\bigl(2^{\alpha}(72n+21)\bigr)\equiv 0\pmod{128},\qquad \overline{bt}\bigl(2^{\alpha}(72n+69)\bigr)\equiv 0\pmod{128}.$$

This is the second conjectured infinite family of congruences mentioned in the supplied text; its resolution is not given.