I would choose low output impedance. You can test with bypassing the input caps too. Those headphones have quite low impedance, I am not sure how well they perform with the Ember. The hd6xx is the benchmark used to design this amp and it should pair very well.
I have never tried Koss headphones. With my hd650 and he400i I can tell appart tubes from different families. All those tubes are fine in my opinion. In my experience the sound really changed for good when I started to use 6SN7 and 6J5 tubes with Ember. Both need adaptors. The main difference with the tubes you mention are a bit better stagging (bigger) and more clarity in my opinion. Bass was also a bit more extended. Note that changing headphones has a lot larger influence than changing tubes.
My tip: if you want to try something different you could try to source the 6sn7 adapter from Jeremy and give a try to a 6sn7 tube (e.g, ken Rad 6sn7gt or Raytheon 6sn7gt with flat plates and support rods). If you don't notice much difference with your HD6xx then perhaps you could settle for a while with those tubes and try to train a bit your ears.
The designer of Ember does not recommend spending a fortune in tubes...they have a relatively moderate effect compared to other elements in the chain