Colour calibration and light source

I'm trying to develop a colour calibration system for dermatological images.
This images are acquired using a video camera equipped with a semi circle of
leds that illuminate the skin.

At the moment I'm following this path:

1) estimate the gamma, by the use of a Kodak Gray Scale
2) build a relation between linear RGB values and XYZ, by measuring a
ColorChecker and using least squares optimization.

The problem is that when going to sRGB the images get too dark (with respect
to the images doctors are used to see on the monitor) and occupy just a
little portion of the color space. My question is: does the fact that I'm
still ignoring the illumination characteristic cause this, or is it related
to the fact that skin colours are really dark and the system is just showing
them highlighted?

Would it be correct to define a specific color space for the instrument and
to convert every other instrument to that one? Note that no one cares if the
image he is seeing is realistic (they have never seen a nevus enlarged 20
times), but the fact is that two different systems shoud show the same
result.

Thanks for your comments.

-- 
/* Costantino Grana                                */
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/* Original code due to Chris Brown... impressive! */