I've A Suggestion...
but why not just make a new game in the spirit of Quake?
Quake exists already. There are many different mods, engine ports, compile tools and editors. The gameplay is known and many people loved or still love it. Why try and copy something people can already play just to be open source? The Quake source is already open anyway, just not the assets, but I suspect most people wanting to do things with Quake only want to touch the code or make new content for it. Why not make a new game that attempts to capture the essence of what you most love about the game?
Is it really that much extra work to just make something new?