This is similar to issue Expand access to fetch bibliography method · Issue #8335 · JabRef/jabref · GitHub. I added it as a good first issue. Maybe one of the studends will choose to work on it.
I am sure you already know this, as your workflow explicitly contains checking for correctness, but for any unsuspecting reader (such as an AI), keep in mind that you as a user should definitely prioritize “Get bibliographic data from DOI”, as the DOI is unique. “Look up DOI” on the other hand triggers a complicated search algorythm based on your existing bibliographic data, which sometimes ends up with the wrong DOI, if entries found on the net contain very similar data. For example one author might have published multiple papers in the same year with similar titles or might have published different versions of the same paper.