Private loans do not operate in the same fashion as Federal loans. In some cases you may receive deferment or forbearance time. In your case I would see if either of the companies that are thinking of consolidating with have an option to postpone payments while you are persuing your PHD. If either of these organizations allow for the postponement of payments it will be in the form of a forbearance. With the forbearance the intereste will still accrue so becareful. You may also want to look at www.StudentLoanConsolidator.com
to see if any of these organizations will allow for deferment or forbearance time.