The following result is due to Kaplan (Theorems 2 and 3 in the paper quoted below):
Let $p<q<r$ be primes, and let $s > q$ be prime such that $s$ is $r$ or $-r$ modulo $pq$. Then the heights of the cyclotomic polynomials of order $pqr$ and $pqs$ are equal.
Using this result for $p=3$ and $q=5$, the problem in the question is reduced to checking it for a single prime in the relevant classes modulo $15$.
This seems feasible to do; I may to so later, then honoring with the request for a Yes/No answer.
Nathan Kaplan, Flat cyclotomic polynomials of order three, J. Number Theory 127 (2007), no. 1, 118--126.