First of all, we are completely changing the topic here. Maybe this isn't a
good idea.
You are correct with zdoom. The confusing combination of licenses requires
non commercial use.
Doomsday is Free Software...if you don't compile it with fmod.
Chocolate Doom is Free Software.
Doomsday is limited to limit-removing wads and wads that use its own content
system. You can't even run boom wads, let alone zdoom wads, in Doomsday.
Chocolate Doom by nature can only run Vanilla Wads.
To run as many wads as possible on a Free Software engine, you will need
Odamex.
As for Assault Cube and Sauerbraten, I'm surprised nobody mentioned Red
Eclipse, as it uses the Sauerbraten engine and has free assets. In other
words, completely free software.