You're looking for a neutral white, warm white, or high CRI LED. The LEDs exist that may fit your needs, but I do not know if the manufacturers of reading lights have decided it is worth the cost and trouble to change their models to use them.
edit: high CRI is not necessarily a warmer tint, but due to the state of the technology at the moment, making an LED with higher CRI also tends to make it warmer looking.
If the manufacturer provides the data, look for color temp below 5000K. Your typical warm white CCFL is 2700K.
High-CRI can be had in a range of color temperatures.
...and I see you referenced that with the edit.
LED manufacturers like to use cool blue because they can get more brightness that way. White LEDs consist of a blue emitter and a phosphor coating that converts some of the blue into wavelengths in the yellow region. Your eye perceives that light as white.
If they let more of the blue through, you can can get a higher lumen rating, and bigger numbers sell more LEDs, even if the light looks like someone's electrocuting a Smurf.
You could always do a retrofit too, with the proper constant-current drive circuitry.
Lighting-grade Rebel LEDs.
(You probably won't want 350mA for a booklight though.
)
On a related note, if you pulse a
very short burst of about 2.5A through a Rebel LED, it's
really goddamn bright.