As the question you linked indicates there is a way to run bughouse engine games via FICS using XBoard/Winboard, which I also explained in my answer to a related question.
However, if all of your engines are anyway running locally, that is neither very convenient nor an efficient way of running such matches, since the server communication in principle is completely unnecessary. Unfortunately, there does not seem to be any tool for engine matches similar to cutechess as there is for other chess variants.
Therefore, a few months ago I started to develop fairyfishtest as a script for testing bughouse (and many other variants) based on and for my engine Fairy-Stockfish, but it should also work with other CECP engines. It currently still has two issues with bughouse rules, but those are far from impossible to solve.
There is also a fork of python-chess that supports bughouse, but there does not seem to be any documentation on it, so I do not know whether/how it can be used for engine testing in bughouse.