Advice with ceiling crossbraces

As you can see in the picture, there are crossbraces in between my ceiling joists. As per John's advice, I would like to screw a couple of layers of OSB right up against the subfloor in between the joists before I put 703 in and then a couple of layers of drywall. I'm figuring those braces are structural and need to stay in some way, but the way they are installed, I won't be able to put the OSB in. Does the OSB have any structural effect that would enable me to remove the braces? Otherwise, will I need to remove and then relocate and reinstall them? If so, I guess I would just trim them to fit, since the OSB will change how they lay. Any advice?

The cross braces are neceassary for the structure. I'd remove them, add the additional OSB and then put them back. You can brace them either by putting what you take out back or by purchasing some timber the same size as the joists and adding it at 90 degrees to the joists. like this cheers john