Also many thanks making me aware of ORCID (together with "DamonHD"). After doing some digging I found ORCID API endpoints which are able to resolve DOIs and PMIDs to ORCID profiles, which is great.
I will take a closer look at the "disambiguation" project you linked to and will see what approach I can take for reliably resolving email addresses to first names (while filtering out non-personal email addresses).
That being said, I fear that resolving non-ORCID + non-email authors using the SerpApi + LLM approach I described in my initial post is still the best shot I currently have.