I would leave it as it is(and replace the SS crown by a GP one). As we know meanwhile, it´s an authentic GP model with the correct reference no. and it wears the correct dial/hands-combo with golden marker-ring, anchor and hands. A SS-case would make a Franken out of it.
If you absolutely want to have a silver case, it doesn´t make sense to plate it again - the case is SS under the GP, so all you have to do is polishing, polishing, polishing and soon the GP will disappear.
A standard polish for SS and/or chrome(cars) will do the job. You shouldn´t use machinery to keep the edges sharp. But IMHO it would be a shame. Maybe selling the GP one for a good price and buying a SS model would be the better way.
Here´s a pic of my Certina DiaMaster(Rado DiaStar 505) with the same case design, but TC-case: