First off, I am not sure I'll ever be a fan from a "fits in with the Warhammer world" perspective. It would of course be silly for you to base your army on what I find fitting, though.
Secondly, if you want to make them look more fantasy-ish I think it can be done, but I think it'll need a lot of work to look halfway convincing.
As it is, the Necrons are a tad to "sleek" and rounded looking for fantasy, I think. Not so much the head and the torso as the arms, legs and weapons. Still, I think they do provide a good baseline to expand upon. Personally, I'd go for bulking them up a bit, give them more square shapes here and there, as well as stick some wood and some cogs in there (no pun!). Especially the wood and cogs part would help immensely to make them look like full-fledged fantasy conversions and not just 40K models. Because honestly, that's what they look like now (my fluff-opinions completely notwithstanding).
I agree with you that it can be done -and I think it can end up as a very unique and interesting looking army- but I do think it'll take a lot of work.
Edit: Nuts and bolts would also be a good thing, especially on the limbs, since they'd break up the sleekness and symmetry of the Necron models (and are pretty easy to do to boot). And do whatever you can to make any guns/mechanical weapons less 40Kish.