Fourteen Doctor Cast...I Think I got it! Plus Master Cast

First Doctor: Octavia, because the comic-given personality matches dead-on, giving her a playfulness and crabbiness that only the First Doctor could have.
Second Doctor: Derpy, who else? They're prone to accidents and distractions, very innocent, highly empathetic, and are somewhat guileless, and yet, they are far more observant than they make themselves look.
Third Doctor: Rarity, who else?
Fourth Doctor: Lyra, who else?
Fifth Doctor: Fluttershy, who else?
Sixth Doctor: Rainbow Dash, who else? They're both so funny on purpose by the writers, but by accident in the contexts of their own universes, and what makes them so hilarious is their unsurpassed egos.

But now we go into undecided territory.

Seventh Doctor: Probably Spitfire, though Twilight is still an option.
Eighth Doctor: Probably Twilight, though Cadence is an option.
War Doctor: Probably Tau Sunflare, though Twilight, Coco Pommel, and so many others, are options.

Back to decided territory:

Ninth Doctor: Applejack
Tenth Doctor: Pinkie Pie, they're very curious, highly manic, and conceal aggression and sadness beneath their smiles, but live to make others happy.
Valeyard: Nightmare Moon
Eleventh Doctor: Princess Luna

Undecided territory again:
Twelfth Doctor: Probably Princess Celestia, though Spitfire, Vinyl Scratch, or some other pony with a whacky, aggressive, and rebellious heart are on the table. (Which is many of them, so that's a lot of options)

I wanted an all-female Doctor cast to maintain the pattern; not a hatred for males, more of a mild r63 type of thing.

So probably it will be:

Octavia
Derpy
Rarity
Lyra
Fluttershy
Rainbow Dash
Spitfire
Twilight Sparkle
Tau Sunflare
Applejack
Pinkie Pie
Nightmare Moon
Princess Luna
Princess Celestia

Trixie will be the Monk; so confident, and good-humored about it, but self-serving and manipulative.

And for the Masters:

Tirek: Rodger Delgado Master, they're both half-funny, half serious, and Tirek's weakened state could be a great equivalent to the Deadly Assassin Master.
King Sombra: Anthony Ainley Master, because they're both so serious and so Dark Lord-ish. Plus, weak Sombra is a nice equivalent of the Keeper of Traken Master
Discord: John Simm Master, because they're both so funny, and just plain nuts!