Menahot 72: Overriding Shabbat

A daf that covers a range of topics at the end of chapter 5: harvesting a crop for the sake of clearing out the area, rather than for the sake of the harvest... The omer is, of course, supposed to be brought from the standing grain - barley, that is. The Gemara then lists several "less than ideal" ways of offering the omer, all of which are included in the Torah's verse - "you will bring," even if it's not in the ideal way of doing so. Also, if the grain for the omer offering was harvested on the 16th of Nisan itself, that would be valid - even to the point of overriding the rules of Shabbat. But how do we know that this offering (and others) would be brought on Shabbat? Plus, more, in case you were missing it, on the Shavuot offering of the 2 loaves.