How can I tell grinder to use more and more threads until it reaches a point where the load is unacceptable?
You can ramp in your threads over time, so that as your test progresses, the load increases. See http://grinder.sourceforge.net/g3/script-gallery.html#threadrampup.py
It will be up to you to determine at what point the load level is unacceptable. Grinder Analyzer might be helpful for that.
Good luck.