Firstly, I would like to welcome you to the MPS forums!
As for your particular question in response, I would say that you chose the following two components well in terms of 20 - 25V input, 6.5V output, the desired 2.6A load current and are able to handle a 22W output with your desired voltage and current conditions.
Both aforementioned parts are able to be connected to external transformers as seen in both datasheet schematics where you should be free to configure each winding respectively. If your transformer has a tertiary winding such that you are able to achieve a low current drain within your desired voltage specs as they would draw 6.5V x 2.6A = 16.9W. So, your tertiary winding should draw no more than 5.1W according to your max power rating of 22W meaning your tertiary winding should have a small enough current to satisfy this.
Although it is not a typical application for multiple windings at the output, this application should work if the power threshold is kept under. May I ask for more information about the application?
MP6002, saves you the bother of buying a FET. Of the two you thought of I would go with 6005 as it is a newer design. How good does the regulation have to be? Getting two windings to regulate is tougher than getting one to regulate, The additional winding has to be 20V or -11? or are you talking two extra output voltages. I would be sorely tempted to pick an off the shelf transformer to get you to 6.5V on the output and then build another converter for the other voltage.
Coilcraft POE51Q-50 might work saturation current is good turns ratio is reasonable. You want to operate fast enough to put this into CCM mode