I think it's good you're doing this. I think I prefer the cardioid overhead option.
If you want the best out of this new setup though, you're gonna have to enter the wormhole. You're getting into infinite variable territory with overheads. There are about a dozen commonly used miking techniques for overheads. They all work, and they all work well, and they all sound different. You're gonna have to find the pattern and distance that works best for your own room.
Or...just keep it simple and use a spaced pair in cardioid. Look up the "recorderman method". It's a good overhead setup for 4 non-matched mics.