Got a book titled "Destiny of the Scotch-Irish: an Account of Presbyterian Migration, 1720-1853, by H. Leonard Porter III. I had high hopes for it (which I may discuss in another post). But a factoid from it:
In 1852 pastors and laymen associated with the Associate Reformed Presbyterian Church (not Michael's denomination) initiated work on establishing a Union Academy in Sparta, IL. By 1855 they'd progressed to having the Illinois General Assembly incorporate the academy, naming twelve people to the board, including "William Rosborough" and "M. Hardshaw". I think it's safe to assume the latter was Michael Harshaw and the former was the namesake of his son, and my grandfather. Unfortunately, the depression of 1857 meant the academy failed.
Unfortunately, the book doesn't provide any more information about the two.
A further note--at the same time the 2nd Associate Presbytery of Illinois was initiating Monmouth College as a coed school. This became the alma mater of my grandmother, Ada Rippey.