The Doctor and The Timeless Child.

(Note: Personally I am a fan of the Timeless Child. If you aren't, I apologize, I'm not debating whether or not the TC is real, just making this theory on the premise that it is.)

While I do like, and believe in, the theory that the bigeneration is just a future doctor being pulled back from the future to help the 14th, and that 14 will regenerate into 15 eventually and get pulled back themselves, there is either:
A. an alternate explanation, or
B. Both theories are true, and one leads to the split, while the other leads to them being able to exist at the same time.

The bigeneration split The Doctor and the Timeless Child.

Think about it:

The Doctor, when they were the timeless child, was chameleon circuited into a Gallifreyan/Time Lord, with limited regenerations. Even though the Time Lords gave the Doctor more regenerations in 'The Time of The Doctor', it's never stated if it's either a limited amount (they've given more regenerations to time lords before, like the Master) or if it's unlocking the TC's unlimited abilities.

While the doctor hasn't been through 12 regenerations since The Time of The Doctor, they might not have given the Doctor a full regeneration cycle, OR he lost some of it with the 'rejuvenating the dying Davros' in 'The Witches Familiar'.

So, what if the chameleon circuit timelord was running out, so the underlying TC DNA 'split' itself out to survive? Now, his memories don't necessarily have to be back, because there could be a difference between 'memory' and 'DNA', where The Doctors' memories have split out, but their memories are still locked in the chameleon circuit.

Thoughts?