Do any ultra quiet ceiling fans that have no motor hum exist?
You might look into ceiling fans with DC motors.  While I have not seen a manufacturer talk about quietness, some reviews I've read talk about quietness.  The biggest attraction to DC motors is the efficiency of the motors, getting more air movement with less power.

My suggestion would be find a local fan / light showroom that has some of these on display that you can try. 

Also, fan speed controls have a lot to do with the fan noise.  A fully variable wallbox style speed control can cause motor noise, but the fan speed controls that have preset "clicks" that you feel when adjusting are made for quiet operation.  I don't know if the remote set you got was matched by the manufacturer or just off the shelf, but that could make a difference.

You also have to remember that some people leave their fans on for a "white noise" effect, which helps them (me) sleep.  My wife insists that we keep a floor fan on for the noise.  Because of this, when it comes to trouble shooting a loud motor then you might not get as much help as you think you would get.

Again, try a fan specialty shop.  The salespeople will know which are quieter and should know more about them than a box store.