riiiight
ambient exposure is normal exposure so controlled by light level (uncontrolled factor) iso, aperture and shutter speed
flash exposure is instant so unaffected by shutter speed, the light level here is flash power and controllable, the other factors are iso and aperture
altering iso and aperture affect both exposures, altering the shutter speed affects only ambient but is limited by sync speed
so if you are at sync speed (1/320th afaik for a 1 series) and want to bring more ambient into the picture lower your shutter speed. If you want to reduce the ambient then you need to reduce aperture or iso, this affects both exposures so you would need to increase the flash power to compensate
if your ambient light was too bright and your flash too dark you would first need to push the shutter to your sync speed to control the ambient, then if you have made the ambient darker than you need open the aperture, or if the ambient is about right increase flash power, or if the ambient is too strong reduce iso/aperture until its right then increase flash power until the flash exposure is correct (in doing this you can run out of flash power)
as an aside the light level produced by the flash is affected by the modifiers used and the subject flash distance so you can make power by moving the flash closer or ditching a mod