Thanks for all the responses, guys, I really appreciate it.
I thought I was on to something - i.e. an explanation for what I think I'm experiencing, but it seems it wasn't that simple.
I don't think my amps are having any trouble driving the S5's. The needles really don't budge (my understanding is that if they were taxed in any way, the needle would start dancing). It might just be that my room is slightly too big for the S5's (not sure)./
I am regularly playing around with speaker positioning, trying to find that balance where the bass remains articulate vs too much bloom. I am hoping to audition some other amps in case there is a more magical combo than what I am enjoying now. Hegel was high on my list until I read that it was on the lean side. Constellation will probably be what I try first as it's supposedly a great combo.
Loving the speakers. Never heard such clean reproduction of vocals, woodwinds etc, but sometimes I do miss the power of the Alexias. Speaking of which, I've never put them back in the system since getting the S5's (they're up for sale). I just might do that someday soon - partly to enjoy the 'power' that they convey so well when I crank the volume, partly to see how I react to what I think it's imperfections are.