It certainly has an interesting take on things, although I must say that I am fundamentally opposed to combining crossovers with AU (which is to a certain extent what advancing to the 44th millenium so you can change things around means).
Also, your timeline is a bit off, Shinji was born in 2001, and his mother died in the experiment when he was four, so he wouldn't be with his foster parents until at least 2005. I also have to ask how the Evas were made if the Imperium showed up after Second Impact. They would, at best, be considered heretical xenos constructs and at worst dabbling with daemonic forces, both of which end in fire.
That said, STOP STEALING THE THOUGHTS FROM MY MIND!
Shinji + Space Wolves was an idea I was playing around with from before Thousand Shinji. I think it works. Part of the original series was showing how Shinji had hidden monsters within him, as evidenced by Unit 01's proclivity to go berserk. The inner beast of the Space Wolves, and their struggles with it, would definitely mesh well with Shinji's character. Of course, the whole thing was being done rather differently, what with Fuyutsuki actually being the Emperor in disguise and playing Gendo and SEELE for the fools before sealing the Evas and their pilots away for thirty thousand years before digging them out to further his experiments with the Warp after he left the Great Crusade to Horus.
I was planning on having Shinji handed over to Leman Russ for training and Asuka sent to Sanguinius.
Anyway, to sum up, there are elements of your idea I like, and elements I dislike either out of personal preference or because they still seem somewhat disjointed and not quite put together fully. You certainly have the essence of an interesting story going, and with perhaps a little more refinement you could make all the pieces fit together quite nicely.