One approach is to use a “slow” binder repo with your requirements in it, and a “fast” repo containing your teaching materials. If you install nbgitpuller into the “slow” repo, it can then be launched on MyBinder and used to pull in content from the “fast” repo.
Here’s a related discourse thread: Tip: embed custom github content in a Binder link with nbgitpuller
Here are some notes I made for myself on this.