How to Avoid a Possible Tie in Future US Presidential Elections Without Amending the Constitution

There is no need to amend the Constitution. The next Congress can just increase the size of the House by one from 435 to 436 to begin with the next next Congress.
BTW, I like the electoral college. I don’t want it abolished by amendment.  I would suggest this change:

Presidential Election Adjustment Amendment

What

• Replace Electoral College, but keep state electoral votes.
• States must bind electoral votes to a President/Vice-President candidate pair among only those on the legal state ballot or that were written in sufficient quantity to win the state-wide contest automatically as the election result is certified.
• The above is true, even if one or both candidates on a ticket have died.
• If a an electoral vote is certified to a presidential candidate that has passed away, the new vice-president shall assume the presidency at the beginning of the term under normal succession rules, and nominate a new VP per normal vacancy replacement procedures.
• If an electoral vote is certified to a vice-presidential candidate that has passed away, the president shall nominate a new VP per normal vacancy replacement procedures after the term begins.
• If both candidates have passed away, normal rules of presidential succession apply, beginning with the speaker of the house upon the term beginning.
• Explicitly state that the “Acting President” cannot appoint a Vice-President or Acting Vice-President.

Why

The electoral collage changes are just for the sake of efficiency and to avoid a potential constitutional crisis in the form of faithless electors. The sections involving death of a candidate who wins are introduced to avoid a potential constitutional crisis by defining the solution ahead of time.