I think the Pathos will probably have enough power - not sure about the Cayin but I have some doubts about it depending on what your definition of "loud" is.
For reference, my room is 14x13 and my speakers (measure) 89dB sensitive and my MC240 tube amp (rated 40W into 8 ohms but does more like 50) can do an average of 95dB at the listening position without clipping - even on the peaks, as far as I can tell. If your speakers are really 86dB, you will need double the power for that same volume level, assuming impedance stays the same.
I would suggest you take a look at the hybrid Unison Research Unico SE. It has 140W and you'll never have to worry about running out of juice. It is right in your price range too. Good luck! Arthur
For reference, my room is 14x13 and my speakers (measure) 89dB sensitive and my MC240 tube amp (rated 40W into 8 ohms but does more like 50) can do an average of 95dB at the listening position without clipping - even on the peaks, as far as I can tell. If your speakers are really 86dB, you will need double the power for that same volume level, assuming impedance stays the same.
I would suggest you take a look at the hybrid Unison Research Unico SE. It has 140W and you'll never have to worry about running out of juice. It is right in your price range too. Good luck! Arthur