Amplifier brand/designer with the most unique and consistent “house sound?”

pass/first watt have more variable sonic signatures across their line than ayre i believe

I would argue that Nelson Pass, especially with his First Watt range might be the most inconsistent. He has become the “Baskin Robbins” of amplifier manufacturers with a variety of flavors, some of which seem to change every month.
Some amp manufacturers have offered factory configurable or even user changeable bridging capabilities, taps, topologies, bias options and feedback controls on specific amplifier models.

How would the house sound of Ayre best be described? 

i recall @erik_squires had a very articulate, apt way of describing the ayre house sound... am sure he will chime in...

If you want honest realism ,and a fantastic value per $$ and great long-standing reputation , over 35 years in business  yet 1/2 the audio community especially the young bloods don’t know of them.
Coda Audio Labs these pioneers designed the classic Threshold Stasis amplifiers back in the 1980s with Nelson Pass, when  Nelson decided to start his own company. Several of Nelson’s design team have been quietly building high end hand built and tested ,and at least 20% less cost  then Pass ,Ayre McIntosh  and at least pas good if not better per dollar spent . Their award winning CSIB integrated amplifier I am waiting on delivery and at $6500 for a true reference integrated ,one of the best kept secrets in all of  Audiophile audio.