Three systems with varying levels of improvement:
"Just A Bit More Rational"
Years ending in 8 or 9. (Such as 2048.)
An open primary narrows the field to the top 3 candidates.
Voters choose up to 2 in the fall election.
States make their own fall election rules, but must appoint electors based on the will of their own voters, not other states' voters. (I suggest states use winner-take-all, to appease the traditionalists.)
A candidate receiving the most electoral votes and a nationwide margin of victory of at least 2 electoral votes wins. (Majority is no longer required due to the fair spring election producing 3 popular candidates.)
Electoral votes as of 2019 total 538, based on each state's congressional representation, and D.C. having equal standing with 3 via previous amendment.
"Compromise Plan"
Years ending in 0, 1, 2, or 3:
(Years such as 2030 and 2042.)
Each state and D.C., having one fewer electoral vote each, would be 487 electors, but instead multiply x 100 for 48,700 points.
Add Puerto Rico, which as a highly populated U.S. territory will have 500 points, for a total of 49,200 points.
The open primary narrows the field to the top 4 candidates.
Vote for up to 2 candidates.
Electoral points must be awarded to all the candidates in each "state," in proportion with the statewide popular vote. Must win the national tally by a margin of at least 50 points.
"The Actual Will Of The People"
Years ending in 4, 5, 6, or 7:
(Years such as 2024 and 2036.)
The open primary narrows the field to the top 5 candidates.
Fall election is popular vote, vote for up to 3 candidates.
Add U.S. territories.
States, D.C., and territories will forward their vote tallies to the congress.
The candidate receiving the most votes wins, if the margin of victory is at least 0.1%.
All years will have these rules in common:
1-term limit, 6 years.
Open primary (all candidates on every ballot), vote for 2 in the primary.
Lame duck House is the tiebreaker when there is no qualifying winner in the fall, usually choosing from the top 2. If 3 or more are within the required margin of victory, the House will hold an approval vote to choose between them. If there's a tie for first, eliminate the least approved candidate, and vote again until there is one plurality winner. (Approval vote is when they may vote for as many candidates as they want.)