Roobarb
Hmm... I dunno, I think the Second Doctor sounded pretty honest when he was counting up his age and came to 450 years old, in Earth terms. I'm betting that all of the First Doctor's adventuring meant he wore through his body a lot faster than the average Time Lord.
On the other hand, I agree about the ego. Especially with the newer Doctors, 900 just seems far too young. And he does always like to be mysterious.
Hadn't he already filled his 500-year diary by that time?
And yeah, I still think he's between 1000 and 2100. He probably claims around nine hundred because it's young by Time Lord standards and he wouldn't want to admit that he's getting old. "The Ten Doctors" refers to both the Ninth and the Sixth as being midlife crises.
And one time, the Fourth said he was about 753 or something and Romana corrected him, but even if she knew his real age, I think they would still be perfectly capable of lying through their teeth to an audience.