The gap for you in this situation is not going to help only cause more problems. Your garment is not "stuck" to a platen as in a normal press and will just lift with the screen and cause severe double imaging.

Thining the ink is going to make it less opaque and harder to get coverage. White by nature is pretty thick.

Good call.   You are only going to get a single print with this, although I suspect you are only getting a single print with your current method, plus driving the ink into the shirt is going to make the white on black look less opaque.   If you are going to do many more, consider setting up a single screen hinge or just cut a piece of melamine that will fit inside the shirt that you can mist with spray glue.  This will keep the shirt from lifting while using off-contact.