Low Powered Tube Amp Distorting High Efficiency Speakers?

Your comment on the distortion showing up in certain high frequencies makes me think it’s a bad driver.  Things like cymbal crashes will sound a bit fuzzy and not crisp. One of the negatives of some high sensitivity designs is that they tend to be less tolerant to clipped signals.  Being just 15 watts I’m guessing you may have had an aggressive listening session or two and pushed the amp, which clipped the signal creating excess friction and thus burned the coils. I hope I’m wrong because replacing drivers isn’t cheap. 

Before starting any troubleshooting process with tubed gear, it's always a good idea to substitute new tubes first (or a stash that you know works). It's an expensive undertaking but unfortunately even new tubes can be defective or out of spec right out of the box. The Russian factories have a very low QC baseline which is why certain retailers (Upscale, TubeDepot, Viva, etc) are worth the extra upcharge for their burn and matching efforts.

Also, EL84's in push-pull pentode mode have very high distortion, up to 10%, once you get above a certain power, usually 10 or 12 watts or so, since all is needed is about a 5 volt swing to produce full power. The 12AX7 have a high amplification factor which can easily swing twice that voltage. So it is possible that you are maxing out at that volume pot setting.

Another possibility is the recording itself. Often vocals are VERY closely miked which can magnify the sibilance. This is true of many rock, pop or new country recordings. Add to that the "loudness wars" recording style that still hasn't gone away in many recordings, or a variation thereof where some popular recordings are mixed and equalized in a manner that makes them stand out when played on so-so equipment like car stereos, cheap radios, ear buds and the like. These effects can really sound nasty when played on a full-range stereo at louder volumes. 

So, the question is: does this problem happen with all recordings or just certain ones? If just some recordings, I think the above comments might explain the issue. If all recordings, maybe it is the speakers, or the acoustics of the room, or a problem with the amp. However, don't forget to look at the source, whether phono, CD or streaming digital. Could be you have the wrong cartridge or phono preamp for your system, or a nasty sounding CD player or DAC. 

Actually that's a good point, hopefully its the tubes or even the source thats causing distortion. Try replicating the problem with a differert amplifier if you have something else available on hand.  If it still exists, it could be the speakers, but you certainly want to isolate the problem first to figure out where its coming from.   

I have a good old fashion Dynaco ST-70 that starts sounding distorted right before the tubes go.  Might try a whole new bank of tubes.