The answer is no, 240 is plenty.
Your amp is not "lowly".
My 40.3XDs are shared as mains between a T+A integrated and a Yamaha RX3080 AVR. I often stream SXM radio from the Yamaha for casual listening and they sound surprisingly good.
Prior to the 40's, I did the same with 30.2 XDs - very enjoyable.
The stands matter, as do cables. I've use Ton Trager, but if you can build something similar from hardwood go for it, but get rid of metal frames and glass.
Buy some decent speaker cables, for example from Frank at Signal Cable. They are not expensive - I own the entry level cables and have compared them with my Acoustic Zen Hologram II and the are damn good for the money.
Then, maybe find a used Hegel 590 or similar if budget allows.