What's the best Line Magnetic SET amp?

Thanks for the response. And yes, you've nailed exactly what I'm asking. I'm not even displeased with my current setup, I just have upgrader's itch.

I am also considering changing my speakers, but I barely know where to start with that. :/

The JBL 4349 speakers use a dual compression driver horn and a conventional 12-inch low frequency cone driver. They are large, for a "monitor," and are typically stand mounted to the JBL JS-150 stand. They do very well with tubes (and also with class-A solid-state) at low volumes and are a bit more sensitive than your Davone Rays, although they don’t have quite the same stylish Eames-ish look.

If your quest is for better low-volume performance, I would suggest trying your Line Magnetics with a more sensitive speaker.

Thanks so much! I'm not looking exclusively for a speaker that performs best at low-volume, but I'm still intrigued. I'll try to check these out.

Maybe a Line Magnetic Analog Sound AS-125 

I own, and like SET amps, but, I don’t think they necessarily sound better than pentode/tetrode pushpull amps.  There are many fine lower powered pushpull amps that sound very good.  To me, the best sound from SETs are achieved with the lower powered tube types, such as 45s, 2a3s and 300Bs, and some of sweet sound and liveliness at low volume is sacrificed with transmitter-tube SETs.  A builder told me that the wiring needed to provide the high voltage on the transformer primaries and other aspects of transformer design compromises the sound of high powered SET amps; this designer generally favors two tubes per channel pushpull (does not like parallel pushpull).

I would suggest looking at amps running nice sounding tubes, like KT 66 or 6L6 tubes in pushpull (e.g. Synthesis Audio A40 amp running KT 66s).  The EL 84 tube, which seems to be ubiquitous in “cheaper” tube amps should not be overlooked as some quite nice amps, like the Audio Note Oto runs this tube.