The electoral college should not be abolished in favor of a public vote. Instead, it should be independent. The electors should be determined and then choose from a collection of candidates. The process would be something like:
1. Every party wanting to recommend a candidate for president should create a platform.
2. The parties will submit the their platforms to the public.
3. Potential presidential/Vice president candidates will present themselves.
4. In September, the public will vote for electors based on the congressional districts - two state wide and one for each representative district.
5. Each party will submit their candidate(s) to the college. Any party or individual will be able to submit a candidate.
6. Candidates and parties will campaign
7. The Electors will have two months to discuss among themselves and their constituents who the best candidate will be.
8. The Electors will convene at the college.
9. Each Elector will cast a vote.
10. If no candidate receives 270 votes, the top two, three, or four will remain depending on how dramatic the separation is.
11. The electors will vote on the remaining candidates.
12. The candidate(s) with the lowest score(s) will be eliminated.
13. The process will continue until one candidate gets 270 votes.
This allows the electors to work together to find a candidate which will most likely be from the party who won the most electoral votes but in consultation with the other electors. The process will help find a suitable president who can work well with both parties even though it is understood the "winning" party's platform will be favored.
Potential presidential candidates and party leaders would be responsible for hammering out a platform then presenting it to the public. Intraparty debates would happen before the parties finalized their platform (by September). Interparty debates would happen after the platforms were presented. The initial debates would focus more on helping to define the platform and commitment to one's party. The final debates would be a blend of why the party's platform is better than the others and how the individual would implement the platform.
This process continues to protect smaller states' rights in that smaller states will have a stronger representation just as they do in Congress.
Dramatic change could be slow with this process but if enough of the population favored a candidate who pledged to shake things up, the candidate would get enough electoral votes to win. Since the electors would not be constrained to a particular candidate, they would be free to find someone favorable to both parties even if large segments of both parties wanted a substantial change - like in 2016.