Oh, and just so no one gets the idea, I'm completely sold on Eccelston wasn't fairly recently Regenerated, I completely accept the possibility that he was. I was only saying it is not a foregone conclusion, it's just as likely he recently Regenerated or that he Regenerated long ago, and just never looked in the mirror. It would have to be at least a little while before meeting Rose though, because the belief is he Regenerated due to some deadly Time War action, and it always takes The Doctor a full adventure to get through his Regeneration Crises/Fits/insanity, etc and Eccelston was already quite himself when he first met Rose, so, it's a good bet, he hadn't Regenerated less than a week before meeting her.
One Day I hope to be the Man my Cat thinks I am
Where are we going? And why are we in this Handbasket?