I've tried ellipsoid collision zones and it still doesn't work because it's target-to-bullets.
If you can possibly to it the other way around then that looks like the best option.
I'm not quite sure what you're suggesting here.
The problem comes from both parties moving at once, so you could move one party, updateworld and process; then move the other party, updateworld and process... all in one gameloop. That way the in-built collisions system does not have to deal with collisions between two moving objects because one type is always static while the other is moving. There are, however, complexities in managing such a system (bullets would have to be offset while you moved the player, to keep them relatively static, for example) and I would personally do everything to avoid it. But it's an option so I mentioned it for the sake of being complete.