Yes I have tried that as well, they currently have the highest number in priority. The strange thing is that if I have an available Commodore and all but one ship is available and I hit assign he still do not get assigned to the Commodore ranked ship but he would happily go to a ship that only require a captain.
What I did was to take a CL ship that normally require a captain and increased this class to require a Commodore. I had one such ship free with no commander and I had one Commodore. I hit assign and the Commodore refuse to take the position. I then lowered the requirement of the class to captain. I then hit assign and now the Commodore would take charge of the ship. Priority was set at 0 on both occasions. There obviously where no other ships to take position on either and no other unassigned commander with a crew training skill.
I don't know what to do really and I never had the same problem before.
The ranks that I currently have are.
Lieutenant Commanders (417)
Commander (139)
Captain (46)
Commodore (15)
Rear Admiral (5)
Vice Admiral (1)
Admiral (0)
First Space Lord (0)
The Vice Admiral has a Fleet Command and so does three of the Rear Admirals, two Rear Admirals are in command of my biggest ships that require a minimum of Commodore.
I now used the "Unassign Type" and assigned the personnel above to their fleet assignment, that left 2 Rear Admirals and 15 Commodores and six ships that require Commodores or higher ranked officers. I clicked the "Auto Assign" and no Rear Admiral or Commodore are assigned to any of my six ships, they get no commanders. All Rear Admirals and Commodores are happily assigned to other ships though.
I then did it all again but lowered the requirement of the two ship classes to captain and this time all my ships got assigned a commander position. I left priority the same as before.