Many threads have been asking for this, but it's all stuff the devs have already tried to give us. Between CGs and the intended use of PP, I would argue FD has already tried to implement the epic sort of goals we all want to see.
For example OP says, "The goal is for all 3 of these factions to all inch their way across the galaxy .. and make it a race. Which side will you contribute to?"
Well the idea of competing factions is all over the game already. Minor factions fight for influence and start wars for control of stations/systems and also star wars to push out waning minor factions.
PP factions compete to hold onto their current systems (undermining, fortification) and to gain new systems (expansion, preparation).
It sounds like what OP is asking for is very similar to how PP is intended to work. Multiple sides and you can support your side however you choose. Of course PP is broken for various reasons, but why would your idea for a "massive CG" work better than what FD has already given us?