Thanks. The HD 206 are already ordered, so I'll have to go with those for now, but I'll definitely keep your tip in mind.
I hadn't heard of "impedance matching". As you can probably tell, this is not an area that I have any expertise in.
These are the specifications for the Casio CDP S350 phones/output jack:
Stereo mini jack - 3.5mm
Output impedance - 3 Ohm Output
Voltage - 1.3V (RMS) MAX
My Sony headphones (which were too quiet) have nominal impedance of 24 Ohm, but so do the HD 201, which were much louder. The 400s (also too quiet) have a nominal impedance of 18 Ohm.
As green as I am about this stuff, I thought that the Sound pressure level (SPL) was going to have a bearing on volume. It's 120dB for the HD 400s, 108dB for the HD 201 and 98dB for the Sony. By that reckoning, the 400s would be the loudest, so that reckoning was clearly wrong. I'll have to read up more about impedance matching.