Give control of the Senate back to the States.
Repeal the Seventeenth Amendment.
You’re not going to get statesmen that way. You’ll just have more elitist parasites choosing elitist parasites and bypassing the only way to stop that: the people.
I suggest three changes: (1) like you, repeal the 17th Amendment, (2) Eliminate the need for 2nd Senator from each state...just go with one, and (3) eliminate any connection of the Senate to the budget.
The only basic functions that I think the Senate ought to be covering: approving cabinet officers for the President, voting up or down on treaties, approving court appointees, and impeachment situations.
If we did these....then you wouldn’t have the whole Senate behaving like lobbyist-controlled nutcases.