The problem with a Takeda timeline is when are you planing it. By the time Imagawa Yoshimoto began his march to Kyoto in 1560, the Takeda was in a triple marriage alliance between themselves and the Imagawa and Hojo. Shingen is not the reckless warmonger his father Nobutora was, he won’t attack if he feels it’s too risky.
When did Takeda did attack the Imagawa in OTL, it caused a rift between Shingen and his oldest son Takeda Yoshinobu who rebelled and was executed. This led to Suwa Katsuyori one of Shingen’s sons to take the Takeda name and be the new heir, yes that Takeda Katsuyori. He was the only suitable and eligible son left who wasn't blind or already in charge of a clan, but by no means was he the inevitable heir.
Also, you need to take actual geography into account the Takeda and held Kai and Shinano both mountainous regions, while Totomi,Suruga and Mikawa were flat and coastal. If the Takeda they risk getting beaten by a much larger and army with good leaders of their own, this is just without the possibility the Hojo don’t join nor do the Uesugi begin to march against Shingen as well.
Now even if for the sake of argument Shingen doesn’t kill his son and manages to at least go westward before dying that still puts the Takeda in a difficult position. The main Takeda Castle was Tsutsujigaski Palace in Kai, they would have move as well. How would a theoretical best case scenario of Yoshinobu Takeda or worse case Katsuyori Takeda rule in this position, I still think that Katsuyori was fine leader on his own, but only really put into a bad position.