Since you asked what direction to look in, here is my recommendation:
A friend of mine had the Classe CA-401 as well. He used the Avalon Eidolons as his speakers though. (Eidolons are notoriously difficult to drive well.)
He tried quite a few monoblock amps before settling on his final amps. (He tried the Kora Cosmos, BAT 150s, Manley Neoclassic 250s, VTL MB 450s, Rowland 501s).
His final amp was the Lamm M2.2s. 220 wpc of incredibly clean, musical power. He said he has found his final amps.
The have an extended treble, with lots of decay, but no brightness. They have a deep, quick authorative bass response, without a hint of boominess. (The best bass he has managed to get out of the Eidolons btw!) And the mid-range has just a touch of that tube magic, without being euphonic. Vocals are sensational to say the least.
After I listened to them, I too fell in love with their sound. (However, I could not afford a pair of new Lamm M2.2s, so I found a pair of used M2.1s (200 wpc) to power my Revel Studios.) The sound is incredible, and I too have found my last amp as well. The M2.1s are withing spitting distance of the M2.2s sound, for less than half the price. I "think" the M2.2s have just a touch better treble. Other than that, not really much difference.)
PS My Lamms replaced a Levinson No. 23 amp, which while a very good amp, is not in the same league to be honest. (And rightfully so, as the Lamms cost 3-4 times as much on the used market.) I love the sound of the Levinson amps, since I had a Levinson amp in my system for almost 15 years.
PPS The Lamms had a bit more power than the Levinson as well, even though they are rated the same. (I guess the separate power supplies in the monoblocks added a bit more power!) Don't worry if you think the Lamms don't have enough power for your speakers. Trust me, they do!