Black is black in the visible spectrum. White is white in the visible spectrum. Alas, there is not much visible light at night, inside your quilt.
When I've done timed experiments on differently painted pots, I found amazingly little difference between white, red, and black painted surfaces. Painted versus bare metal had huge differences, but the colors all seemed to be pretty "black" (high emissivity) in the infrared spectrum.
High emissivity means that the colors ABSORBS a lot of the IR (85-95%) AND that the color EMITS a lot of IR (the same 85-95%).
The quilt is only warm to the extent your body has warmed it ( i.e. the quilt is cooler than your body). So you want minimal radiant heat exchange with the quilt. Think Thermos bottle with the silvered liner. So you want metallic reflective material, rather than any color of paint, unless you can find some paint that is "white in the IR spectrum" (has low emissivity in the 4-30 micrometer range).
Frankly, the crinkling of a metallic liner and the minor effects it would have, would make me go for a black-in-the-visible liner so that it can be inverted and dried quickly in the sun.