A question about impedance on a multiplexer
Apple earbuds are 23 ohms, Audio-Technica ATH-M50 is 38 ohms, Sony
  MDR7506 studio headphone is 63 ohms and more pro headphones have
  higher impedances.
  
  How do I deal with this?


I'd add a small stereo power amplifier at the output just prior to the headphone socket like you mentioned. You don't really want to be passing HiFi currents through an analogue switch like this because of non-linearities in the channel. 

Or just swap-out the part for a type with much lower impedance and see if it sounds OK. The MAX309 is functionally compatible and has impedances about one-tenth of the part you are using for instance. However, if you do go down this route you will need to think about making your capacitor signal couplers bigger in value.