Prob cheapest is a Pi3A+ with 2x I2S Mic with software AEC as for many uses its essential but hardware is extremely costly.
As posted here.
Sort of dissagree about changing wake word as do you call your dog a cat because you prefer the name?
The load to provide phonetic custom based wake words is huge compared to specific trained models and now that server TPU hourly charging is so cheap fragmenting accuracy for a single phonetic customisable model rather than a choice of specific trained models is definately the wrong direction.
Satelites can be extremely lean and making the KWS lite has huge impacts on cost in this mode.
Unfortunately the importance of collating datasets is hardly mentioned as if they where available easily accesable with accompanying tools models would come in droves.
Supplying models without the datasets is as closed as suppling binaries without code.
Mycroft need to look over there shoulder as there are alternatives that in implementation have probably overtaken them.
If they had a community portal it would probably be a no brainer as there direction with many aspects is superior, but seem business orientated.
Mycroft in a many distributed form is fat and expensive but hopefully we will see a more partitioned form soon that is official.
There is also the RockPiS which is a Pi3 perf 64bit Soc with built in audio and DSP VAD for $15 that prob needs exploring.
The skills section and community in Mycroft is still awesome but voice AI has rapidly changed, presuming with the new CEO and the new vacancies much is going to change as currently the hardware proposed is very hard to justify with what is available elsewhere.
Pi3A+, 2x I2S mics or USB stereo ADC soundcard, 40 watt amp & Speaker is approx $60 and about as cheap as I can make it.
But the hardware that seems to be proposed in terms of cost for a number of units to be littered around the home is definately an eye roller.