#the drumming

Putting Dhawan's Master between Simm and Gomez does a huge disservice to all three incarnations.

Missy's entire personality is carved out of Simm!Master's character arc. And Dhawan's personality is carved out of Missy's character arc.

His incarnation was all about exploring why the Master turned to evil in the first place, while also being too spiteful to consider reconciling with the Doctor. Hence why he's enraged at the very thought of the Doctor's forgiveness, and chooses to die just to hurt the Doctor that little bit more. He finally discovers the truth of what he is, and while he rightfully directs his anger at Rassilon rather than the Doctor, he's still too spiteful to consider standing with the Doctor, and murders his future self to prevent it.

So, he wakes up as Missy, with no recollection of the events on the colony ship, but plenty of memories of The End of Time and an understanding of why she is the way she is. But now the spite and pettiness has gone. Now she understands why their friendship went sour in the first place, she has no reason to fight and oppose the Doctor, so she seeks instead to reconcile with him, albeit in The Master's typically twisted way, and with her typical narcissism. And in the end, she becomes someone that is not kind, at least not in the way the Doctor wants her to be, but values their friendship enough to try.

Sticking Dhawan in-between them throws that character arc away completely. If Simm regenerated into Dhawan and discovered the Timeless Child, he would still be insecure and bitter that he couldn't be the Doctor's equal, but the spite and arrogance from Simm would've boiled over to the point he would've killed the Doctor straight away. (This would've happened with Missy too if she'd discovered the Timeless Child early in her incarnation). It's only because Missy so badly wanted to stand with the Doctor as equals ("A friendship older than your civilisation and infinitely more complex") that he's so hurt that they aren't equals at all. That's why the only way out for him is designed for them to die together. Because he doesn't want to live if he can't stand with the Doctor as her equal.