I initially avoided atoms back when i built it, after reading a review/article by Toms Hardware, which showed a 45nm Core2 plus G31 chipset could more or less match the Atoms in idle power, but yet had a bit of grunt in reserve if it happened to be required.
You shouldn't over-generalize because very different products get the same brand name and even (in this case) the same CPU architecture.
Atoms are unsuitable for your application (unlike AMD's equivalent) but the more efficient Atom solutions are very efficient indeed... and that was already true back in the day. It's just that the cheaper desktop Atoms are not supposed to be efficient, just very cheap.
I've not found all that much info on how little power you can get away with on more modern systems.
Clarkdales go down to 15W, Sandys to 13W I guess and Ivys to about 10W. But most systems based on those boards burn a lot more. I'm talking Intel and MSI boards with few features, BIOS tweaks and/or minimal peripherals as well as extremely efficient PSUs.
Perhaps some suggestions on what boards would pair up with the G6950, and provide minimum energy consumption, plus a decent set of twiddles in the bios to allow me to undervolt the CPU etc?
Any basic Intel or MSI board with the least features (like the current Hxx chipsets).
It's not worth buying an obsolete board though (unless you can get it really cheap). Current gear is better and the cheapest current CPUs are really cheap (look up the G530, which isn't even one of the crippled models). The cheaper Ivy boards aren't that expensive actually but you can always get a Sandy. It would still be better than a Clarksdale.
Manual undervolting is over-rated. The lowest idle power consumption are typically achieved without manual undervolting. Undervolting is useful to lower power consumption at load however.