Currently, it seems that it is not possible to use the Jenkins Remote Access API when authentication with the Google Login Plugin. I believe that allowing such access would be beneficial.

Indeed, to me (no experience in Jenkins plugin development), it seems like implementation for this functionality has already been started but is still commented out and below a TODO marking here.

The way that the GitHub OAuth Plugin handles this case (by allowing username/password to be GitHub username and GitHub token) works very well for us.