Refinishing can be a long process because a lot of it is done by hand.  You can have it refinished through your pro shop (which may take 8 weeks) or through the Scotty Cameron "Custom" shop which takes about 4-5 weeks.  If it is usable, you may want to wait until the season is done or email the "Custom" shop  to see if it can be done any sooner  than 4-5 weeks.  Their email is: customshop@acushnetgolf.com.

Here is a link for the Cameron Custom Shop.  While there you can have it personalized or customized for you as well.  They do great work and your putter will come out looking good as new

http://www.scottycameron.com/customization/default.asp

I agree.  You should send it to the custom shop.  Pro Platinum is a tough one to do by yourself.  I've gun blued some putters, but I wouldn't mess with remilling or refinishing with Pro Platinum.