How to find the most related publications for a batch?
What you are asking for might be possible by writing your own program (e.g. in Python) to access the Google Scholar API.  In fact it would make a good assignment for a Python programming / Text processing class. But unless you are a programmer with extra time on your hands, you shouldn't attempt it.

For what it's worth, I almost never use "related articles" feature of Google Scholar.  The few times I did use it, there wasn't always such a close relationship, and it certainly didn't bring up the articles that I saw as most related.

I don't think there's any substitute for reading the papers, at least the important ones, to find the most salient related papers.  I do this both through direct citations and also by finding key terms that I use for new Google Scholar searches.