Howling:Missy, Doctor, Master, and Valyard?

This theory is going to be a bit of a doozy, so bear with me.

So, when the time lords beamed the Doctor a new set of regenerations, what if the regenerations weren't really all that fresh?

From previous examples, we have seen that regenerations can be both given and stolen between Time Lords. By time lord standards, the equivalent of an execution would be killing said time lord and giving the remaining regenerations to another time lord. The last we saw of the master, he ended up being trapped in some of the closing moments of the Time War with Rassilon, and a number of other high up time lords. So what, in giving the The Doctor more regenerations, they were killing two birds with one stone in executing the master at the same time?

So how does Missy fit into all this? Well, there has already been some speculation of her being the master, through the logic of "Missy" being a shortened form of "Mistress." If the time lords beamed the master's regenerations into the Doctor, what if the Master is still rattling around in the 13th Doctor's subconscious in the form of this "Missy" character? It would explain the whole "accent" link between them, and also, the darker self-centered personality quirks that are manifesting in the new regeneration, as a representation of a greater conflict between the Doctor and the Master for dominance over the Doctor's body. My current theory is that at some point, "Missy", being a hybrid of the Master, and the darker parts of the Doctor's subconscious are eventually going to find their way out of the 13th Doctor's head, manifesting as the entity known as the Valyard. So what do people think of this idea? Too far out there, or is this a pretty solid theory?