but this scenario is telling you that there is virtually no grip from the tyres, so don’t expect much to change...
On the contrary. Expect a huge change if you:
1) "In all cases, brakes and reverse should be applied smoothly. If there is any concern with directional controllability then reduce or cancel reverse as necessary and reduce braking until control is regained. Then smoothly re-apply brakes and reverse if necessary." (Safety First Magazine - issue 12 page 11)
2) "As required, or when taking over from autobrake, applying brakes normally with a steady pressure; • For directional control, using rudder pedals and differential braking, as required (i.e., not using nose-wheel-steering tiller); • If differential braking is necessary, applying pedal braking on the required side and releasing completely the pedal action on the opposite side; and, • After reaching taxi speed, using nose-wheel steering with care." (Getting to Grips with Approach and Landings accidents reduction - Page 19)
Or carry on with full reverse and full brakes whilst you push yourself off the side of the runway.