The ENO crank is not a road double actually, it is a mountain double crank. VBC cranks are offered in two variations - road and mountain. ENO cranks are the single speed and mountain double arms. The cranks I have are designed with wide chain stays in mind, so this should work. I always knew the Atlantis had wide stays, but after seeing a few photos of this combination online, I wasn't expecting any troubles.
The only reason this is getting complicated is because the instructions provided by White Industries themselves generated a BB length that simply made no sense - well over 140mm.
So in some ways, I agree - my first step was to use the manufacturer-provided guidelines for calculating bottom brackets. This generated questionable results, so that lead me to option two: ask the owners group if anyone is running the same combination and can share their BB length. Since that didn't turn anything up either, I asked the manufacturer if I was using their formula correctly. And then, like you suggested, I'm on to option 3 - go to a shop, and trial and error.
I am well aware that bike shops charge for labour by the hour and it's a valuable service. I spend a significant amount of my money employing my local shops for this exact service, so there is no need to preach the value of paying skilled craftspeople to me. I am part of the choir. The reason why this thread has rambled on is that there never should have been a need to employ any skilled mechanic, much less go into a trail and error mode and waste money buying a bunch of cheap bottom brackets as a means of finding the right length, because calculating BB length is easy with some simple math. I've done it for all my bikes for over a decade. I pay my bike shop to do things I can't do, and order components locally whenever possible. I'm building the Atlantis myself because I enjoy it, not simply to save money or because I don't value skilled work.
I manage a graphic design studio and have the exact same understanding of the value of time as you do in architecture. That's why I came to an owner/enthusiast group first, which doesn't cost anyone anything, then contacted the manufacturer of the crank second (simply asking if I was using their published guidelines for calculations correctly) and only contacted Riv for advice after even my own local shop mechanics (who I pay) were scratching their heads.
Anyway, you may be glad to know I now have a pile of unused bottom brackets as well as a number of other components for the build purchased from my local shop (shop wins), some new, smaller white industries rings and BB on the way that will enable a much narrower BB (White Ind wins), already had ordered a number of the components for the Atlantis from Rivendell directly (Riv wins), and will soon be spending my time riding blissfully into the sunset instead of justifying my query here (we both win!)
Problem solved, now lets go ride some bikes.