SPLAININ TO DO: THE RECASTAWAY KNOWN AS DOCTOR 1B

Two items of note from the TARDIS Data Core wiki:

The Time Lord named Handrel claimed that a single incarnation of a Time Lord could live for around ten thousand years. 

(PROSE: The Time Lord's Story)

Of course, as this information comes from BookWorld, it might not apply to the lore of the Time Lords to be gleaned from the greater TV Universe.  But since so much of the general information... information... information about Gallifrey is shared between the various metafictional universes, I see no reason at this time to debate this possibility.  It's just that it's not something we're likely to see happen with any other Time Lord save the "Tenth" and the "Eleventh" Incarnations.  And taken to its limit with the "Tenth" because of interference by the Master, it might not be something devoutly to be wished for.....

And in reference to the First Incarnation:
This incarnation regenerated when he was 450-years-old. 

(PROSE: Iceberg)

Again, I see no reason why this should not accepted for consideration when it comes to the televersion of the First Doctor.

[A quick O'Bservation: Any numerical identity of the Doctor's incarnations after Number Eight will be encased in quotation marks because of the War Doctor.]

Once upon a Time, your faithful Claviger (aka "The Monitaur") tried to come up with a splainin for the recastaway of the First Doctor in the 20th anniversary episode "The Five Doctors".  But it was complicated, involving the Earth Prime-Time Susan Foreman, now grown older, but teamed up with the Doctor from another TV dimension.

Since then, I rely more on Occam's Razor to keep it all simple in my head.

To that end, Toobworld Central has often accepted recasting to cover up discrepancies caused by the aging of a character.  With the upcoming spin-off from 'The Big Bang Theory', Laurie Metcalf's daughter will be playing a younger version of her character as Sheldon's mother.  In 'Lois & Clark', when Jimmy Olsen was rapidly aged, the producers cast Jack Larson - the Jimmy Olsen of 'The Adventures Of Superman'! - to play the older version.  Who could find fault with that?

The best example of this within the context of 'Doctor Who' would be for Amelia Pond.  As a child she was played by Caitlin Blackwood and then her grown-up incarnation was played by Karen Gillan.  Most fans of the show know this, but Karen and Caitlin are actually cousins so the resemblance was closer than most.

Therefore, I think that's the route I need to take with the recastaway of Richard Hurndall for the late William Hartnell as the First Incarnation of the Doctor.  We saw him at an earlier stage in his 450 years - before the toll of his worries creased his face, before he had begun losing stature due to age and loss of bone density.  (Hartnell was 5'-8".  Hurndall was about two inches taller, I think.  Peter Davison is listed online as being 6'-1" and in this picture with the two of them standing together, Hurndall is only a few inches shorter.)

The Doctor's granddaughter Susan Foreman was definitely older than we last saw her, of course (after he abandoned her to be with the young man she fancied.)  I think what happened was that the First Doctor crossed his own time-stream and reunited with her at the wrong point in Time, just before they were scooped up for that multiple Doctors adventure.

None of the Doctor's incarnations remembered what happened during that time when they were all brought together because of Borusa's evil plot.  But something must have tugged at the First Incarnation's memories, because in later years he became adamant that History could not be rewritten, not one line.  

It's almost as complicated a splainin for the recastaway of Doctor 1 to Doctor 1B as was the original, but it should work better than delving into alternate dimensions.

BCnU!