If for some reason room layout this is undesirable i would screw another 3 4 layer over top.
Installing flooring parallel to joists.
Installing hardwood floors against a hardwood floor.
Installing rim joists the rim joists that run parallel to the floor joists are installed with the joists.
Installing solid hardwood parallel with floor joists.
The other option assuming you have access to the open joists from below is to install 2x4 blocking between the joists 24 inches on center.
The perpendicular rim joists the ones that cap the ends of the joists can either be installed as the floor joists go in or be added after the joists are in place.
3 4 flooring should be installed across the joists.
I agree that if you have less than 3 4 of you should definitely run the flooring perpendicular to the joists or at a 45 degree angle.
I will be soon laying my 3 4 prefinished strip maple flooring.
This is on the first floor the sub is plywood and the house has an unfinished basement.
What you have with 5 8 is not near adequate or stable enough to support you floor and everything else you will put on it.
We installed our hardwood flooring parallel to the joists.
Most flooring installers will lay the flooring parallel to the long length of the room to avoid the ladder affect.
However if you have 3 4 plywood or osb you can change the direction.
There is a steel i going through the middle of the house.
The span is about 14 feet from foundation.
If raising the floor height is not a problem you can install a layer of 1 2 inch plywood over the existing 3 4 inch plywood.
As an alternate you could install the floor diagonally.
I have 9 1 2 i joists and 3 4 ply subfloor.
So my plan is to block the joists and replace the tired ugly flooring with something new run perpendicular to the windows but parallel to the 2x10 joists.