Improve it? He was dead against it without it. A deadly defect like that is a lot more active than the passivity you suggest...
Were that the case, he would have publicly criticized the Virginia convention for ratifying the unamended Constitution in July 1788.
What was his response to the ratification? He wrote a private letter, which your source quoted, to James Madison saying: "I hope, therefore, a bill of rights will be formed to guard the people against the federal government" and he did not write a public "I am dead against this Constitution!" remonstrance.
He "hoped" that the amendments would be made. That's not a particularly aggressive stance, but it is a wisely considered one.