what is transformer 9-0-9
This might help. It's a very peculiar supply as the device connector is not your typical wall-wart. It has something that looks like a telephone or CAT-5 connector, and each tap has two wires.
The supply only has the transformer; all other components are on the board.
According to the top of the power supply case, which I didn't notice before, there is a little drawing of this connector and it says Pins 1+6 center (white and blue), Pin 2+5 9vac, Pin 3+4 9vac.
This would seem to confirm that I need a 9-0-9 as a replacement; I don't know if buying an 18vac wall wart and cracking the case open would reveal a 9-0-9 transformer that I could just connect up to this peculiar output plug or if it would just be an 18+0 transformer with 2 taps, which I probably wouldn't be able to use as a replacement.
Getting it rewound is certainly not something that I had even thought about but it is an option, although I would have to go search for someone who could do that. I don't know if it would be prohibitively expensive for a custom job like that.
Thanks
Phil