however it would take a constitutional amendment to modify federal elections criteria
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Exactly. Unfortunately all elections are controlled at the state level. House members and Senate members are elected directly by a vote on the state level. In the Presidential election voters are voting for representatives to the Electoral College, who can technically vote for whomever they choose.
There needs to be an amendment to federalize House, Senate, and Presidential elections and hold them on a different date that state or local elections, with no absentee ballots except for legitimate reasons allowed.
The amendment needs to specify that electoral ballots be vote according to the outcome of the vote in each Congressional District (whoever wins the majority of votes in a Congressional District gets that Congressional district’s Electoral Ballot). The two Electoral Ballots generated in each state and allocated per Senator should be decided by the legislative body of each state.
Actually, it wouldn't. In 1826, Congress abolished property qualifications for federal elections, and in 1841 (or 1846, senior moment here), Congress set the date for federal elections to the date we still use today.
On the issue of federal elections, Congress has complete control of the process, and no amendment is necessary.
For your proposed changes to the Electoral College, that's another story. You're right. The Constitution gives the state legislatures plenary authority to determine how electoral votes are to be handled, and your proposed change would require an amendment.