Bauerp
My room is just over 4M wide, and just under 6M deep, with the speakers firing off the short wall. I've two openings towards the rear of the room and one on either side.
There's more than one way to skin a cat, as they say. I'm thinking the IIIs & your amp should do OK. i ran a BAT 60spc tube amp on mine and they sounded fine. Lots of volume. Not a lot of bass though. good punchy bass on tube amps seems an elusive thing generally speaking.
For me in my room, 92 - 94 db (avg), is more than I can handle for extended playing. maybe a song or two, but no more, then I need a break. the BAT vk60 did that on my sonata IIIs.
Consequently, I'd say SS is NOT a prerequsite for the Sonata IIIs to provide you volume. That's easy!
To do their best however is subjective! The real answer is going to be determined by your own tastes and preffs.
As far as I'm concerned the sonata IIIs are great speakers, period. given they're also in the over $7K retail range, having something comensurate to push them with might well be inorder too... I've found I can live pretty well with amps in the $5000 - $6000 range very often. More or less expense there ain't a bad thing either, I suppose, it's just my experience and was said above... "What sort of 50 wpc amp?". they ain't all equal. (also do try the 4 ohm taps off the amp, as well as the 8's if you get the Sonata IIIs... just a thought.).