To be precise, the meanings quoted probably arose because of the mythology of Draupadi having adopted that name. The literal meaning probably was more like `the daughter of a farmer' from the Rgvedic word sIra meaning plough (the same sI appears in sItA and sIman) and the Indoeuropean root occurring in Sanskrit dhR to hold. Of course, the great plough holder from mythology is balarAma, kRSNa's elder brother, who could bend the path of rivers with his plough, but I have never found a relation between that myth and sairindhrI.
The word is most often used to mean a menial maid-servant, especially in women's quarters. In a caste based society, most guilds were explained as `mixed castes', and this was no exception.
I am surprised that it is popular in Eastern India: the name definitely sounds a generation too old.