The Senate rules have been changed by a simple majority, but that was early in the history of Congress; like about 10-15 years in. The "unlimited debate" paradigm came about when the motion to call the question was eliminated in, IIRC, 1804. That rule change was adopted by a simple majority.
The Senate is a truly dysfunctional body. Congress has run the country into the ground. There isn't enough shame and opprobrium in the universe to give Congress the legacy it has earned itself.
I quit watching the Senate close, about 4 years ago. I suspect you are correct that he doesn't have a simple majority to go along with his plan to toxify the body.
“his plan to toxify the body” or ‘de-toxify’?
The Senate’s problem is that it’s a ‘federalist’ body in a centralized media world. The national media can change a Senate race by ten points.
The Senators’ special privileges are those of representatives of the parts of the republic- the states- in a world where states no longer matter. What matters is only what the national networks say matters.