I believe some very interesting facts came up already. Bipoles should work pretty well for many genres like RPG, RTS, Racing/Driving Sims, etc. creating an enveloping sound field. Now, where positional audio is key as in FPS, DogFight Sims, etc. you could do better with monopoles or more directional speakers but that's not to say it will be unplayable.
In the end, you'll always have to compromise and decide where value is and what is acceptable. Some criteria may be:
Are you into competitive gaming or just for fun?
What genres do you play the most?
If you were to define percentages, what would they be? For example, Movies/Music/Games 60/10/30?
I don't think moving the speaker so the woofer points toward you and the tweeter away will work. It may be worth a try but they were not engineered that way.