All private stock orders are done through the dealer. Contact any dealers you would like to buy through, and they will give you a quote. The quotes will NOT be exactly the same as the dealer will decide how much profit they want to bake into the same order. You CAN get quotes from multiple dealers, so don't be afraid to do so. AFIK, quotes cost nothing. As for the timing, I would bet the dealers will be telling you an estimated time, and they will have no control if it takes a lot longer. Regarding the options that are available, I can not speak to that as a lot of people have been getting a lot of "no" answers to requests over the past 2 years or so, supposedly because of the "back log". Whatever the case is, your dealer(s) will be able to sort that out for you when you request a quote.
So how do you order a private stock? With a lot of patience as well as willingness to not get EXACTLY what you want in some cases! Hope it all goes perfect for you!!!