  We adapt the PDE approach of Guo-Phong-Tong and Guo-Phong-Tong-Wang [17, 18]
to prove an $L^\infty$ estimate for transverse complex Monge-Amp\`ere equations
on homologically orientable transverse K\"ahler manifolds. As an application,
we obtain a purely PDE proof of the regularity of Calabi-Yau cone metrics on
Q-Gorenstein T-varieties.
