A quick update.
John and Anne's children are as noted above by Adee 101, and the Anne Winters and John Sheridan marriage was on 4 Sept 1856 at Monasterboice. Anne is the daughter of Anne Mullen and Peter Winters and was baptised in 1837 at Monasterboice.
Adee 101 also found Rose Ann's marriage in St Mary's Drogheda on 23 June 1890 to Thomas Kenny of Whicklow. I have tried to trace them in the 1901 and 1911 censuses but to no avail. Francis and Catherine Sheridan were their witnesses, however, so we have moved on from knowing they were alive when John signed up in 1883!
After years of stagnation, we have made huge leaps forward in one weekend. Thank you to all who have helped. If there's anyone out there who can take the story forward (or indeed backwards!), the search goes on...