Thanks everyone for your time, but I found the cause of the issue.

When I was adding the widget tree to the question, as I was asked, I noticed that somehow a FutureBuilder had snuck out of the MaterialApp: an issue perfectly consistent with the missing Directionality widget that seemed to be the cause of the grey error screen.
I then pinpointed the FutureBuilder and its Future, and noticed that it could actually return a simple Text widget that would end up being shown without the necessary support of MaterialApp and the likes.
Today I managed to connect to that peculiar PC, and I installed a beta version that avoided showing an orphan Text and, et voilà, the real error was shown in the GUI (which had nothing to do with Flutter and I already managed to solve).
So, thanks again for being my rubber duck.