The Monsey Times newspaper printed a posuk from Sefer Vayikra in Hebrew that contains the Shem Hashem. It is at the end of the Letters to the Editor on page 4.
You said that already.
Sadly, putting the newspaper into a shaimos bin at the beis medrash may be the same as putting into the blue recycling bin at the curb. There have been so many recent episodes of bags of shaimos turning up near landfills, in abandoned rental trucks or simply strewn on the street.