No organised recovery of the entire plane has been attempted since the crash. The info about 13013 disappearing into the undercast in a spin makes perfectly sense since the shaddered remains indicates an almost vertical impact. I'm guessing that the procedure must have been something like recovering the bodies, weaponry and munitions, log books and anything containing military or personal information, that wasn't destroyed in the explosion and fire.
The wreck is relatively accessible, half an hour on foot away from the nearest sheep farm of Ipiutaq. Remaining removable parts have been collected by locals over time. As you can see on some of the photos quite a lot of locals and tourists have made inscriptions in the paint work.
As seen on photo in link below, airplane parts also made their way into the local architecture. The window stems from the "Alabama Exterminator" a B-17E en route from Goose Bay to Bluie West 8, Kangerlussuaq, in 1942. It ran out of fuel and had to ditch near the town of Aasiaat. This aircraft has been recovered.
https://picasaweb.google.com/lh/photo/_ ... directlinkhttp://www.warcovers.dk/greenland/crash260642.htm