I have a theory about the War Doctor regeneration. When John Hurt's character goes gold, his face gets the close-up, it cuts away quick after a little bit of a morph but those are clearly Eccleston's eyes.
So, things we know:
1. They have a whole season of footage of Eccleston
2. There's no way in hell he'd come back to film something new for the show, even for a brief shot
3. They probably wouldn't be able to use footage from another show, either because of permission or budget
4. There's not much deleted material in the sense of entire unused camera angles. I've heard they only shoot what they need, and the schedule is fast-paced and somewhat taxing, even grueling.
Conclusion:
The shot of Hurt/War Doc looking upward toward camera was blocked, staged, and angled to match an existing Eccleston shot from Season 1 that they re-used as the post-regeneration 9th Doc, and it's in an episode, and likely they didn't want to imply Eccleston's involvement because of the bad relations they have with him, so they didn't use his full likeness, just an implication of it. Thus, if "we" find the original clean shot, "we" can extend the effect to show the full transformation into Eccleston. I'm going to scrub through the episodes tomorrow when I have time and see if I can catch it. If I'm right I'll find it. If I'm wrong, oh well, it's worth trying.