[argyllcms] Best way to proceed?

So, I've made some progress in this project, but I'm hoping that I'm not -- as I think I am -- doomed to doing everything the old-fashioned way.
Attached is a small sRGB JPEG of one of the works. The art is pretty close; I think only those with a critical eye would be able to tell the difference, and the conversion to an email-friendly attachment has probably altered it about as much as it's off from the original. The print is a bit dark...I need to crank down the backlight on the display.
I did all the color correction by fiddling with the sliders in Adobe Camera Raw. And, as a quick glance at the ColorChecker will show you, I did a *lot* of fiddling.
I then shot a couple other pieces with the same lighting and ACR settings. They're also in the ballpark, but still in need of tweaking. 

Is there any hope of doing this colorimetrically?
To make matters worse, some of the woods are very slightly iridescent, and change luminance (mostly) and hue (slightly) rather noticeably with shifting lighting angles.... 

Cheers,

b&

JPEG image

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