This apparent fixation of Nancy Pelosi's (hic-up) is a bunch of road apples. Furthermore, even if the Senate was able to pass a separate vote to exclude a person from office, what is the mechanism to enforce it? I don't believe there is one.
Article III, Section 3, para 7:
“Judgment in cases of impeachment shall not extend further than to removal from office, and disqualification to hold and enjoy any office of honor, trust or profit under the United States: but the party convicted shall nevertheless be liable and subject to indictment, trial, judgment and punishment, according to law.”
Notice that the one convicted can be permanently disqualified from office.
The problem is that you’d have to have a slate of electors on file should the write-in candidate win. Remember, we don’t elect a President, we elect electors who elect a President.