I am trying to count commits for many large github repos using the API, so I would like to avoid getting the entire list of commits (this way as an example:
If you're looking for the total number of commits in the default branch, you might consider a different approach.
Use the Repo Contributors API to fetch a list of all contributors:
https://developer.github.com/v3/repos/#list-contributors
Each item in the list will contain a contributions field which tells you how many commits the user authored in the default branch. Sum those fields across all contributors and you should get the total number of commits in the default branch.
The list of contributors if often much shorter than the list of commits, so it should take fewer requests to compute the total number of commits in the default branch.