Finding motors

I suspect you may need to over-power your motor to get the output you want - with a small risk of overheating the motor.

Is there a limit to the physical size of the motor?

It's a long time since I was familiar with the wattage numbers but a low voltage (i.e. 3v or 5v) 540 size motor should meet your need. For 27watts at 9v you will need about 6 amps (allowing for inefficiency) and even the smaller motors can take that for a limited time. I have some smaller motors that could take 9 amps - I think they may be a 230 or 250 size, but I can't be certain. (And I don't know what those numbers refer to).

...R