When I machine press fits, my general rule of thumb is 5 tenths to 1 thou squeeze per 1.0 inch of diameter depending on my mood and the part and the phase of the moon. In you case, with a thin, hard lock ring, I'd want no more than 2 thou squeeze. Just over a thou would be best to not worry about cracking the ring.
Those two numbers you put up are miles away from each other in the press fit world. The shaft diameter you put up is most likely 35mm rather than 1-3/8 oversize. A majority of bearings out there are metric regardless of OEM application. The retainer ring should be 34.95mm ID or 1.3765" ID