That is a fantastic offer josey, however, I am not completely sure what information you need. As you mentioned before, if John Harding died in service, then there will be no discharge papers for him. However, William Morris survived and came back to England, so there is a possibility that his discharge papers exist.
William Morris was back in England by the 1881 census, married and with children to Letitia. They are living in 'barracks' Sheffield. William's occupation is given as 'Color Sergeant 2/19th Regiment. By 1891 he is living in Hunslet, Leeds, and his occupation is now 'Store Keeper'. Presumably, therefore, he was discharged between 1881 and 1891.
According to the Nation Archives website you recommended, it says
'Soldiers discharged 1873-1882
Look in the 1873-1882 section of the WO 97 class list (WO 97/1722 to WO 97/2171 ), under the appropriate branch of the army (Cavalry, Household Cavalry, Royal Artillery, Royal Engineers, Foot Guards, Infantry, Army Service Corps, Army Hospital Corps, Military Staff Corps, Rifle Brigade, Colonial Regiments (e.g. Bengal, Cape, China, Ceylon, Canada, Malta and West Indies), and miscellaneous units). Some discharge papers have been misfiled, and are now in alphabetical order in WO 97/6355 to WO 97/6383 . '
That sounds quite complicated, as I don't know what branch of the Army he was in, how do I find out what branch of the Army he was in? Are all of the Green Howards in the same branch of the Army?
After 1882 it seems a bit simpler:
'Soldiers discharged 1882-1900
For this period all discharge papers were filed alphabetically, for the whole army (WO 97/2172 to WO 97/4231 ). Some discharge papers may have been misfiled, and are now in a second alphabetic sequence in WO 97/6355 to WO 97/6383 . These documents are seen in the original, and are ordered on computer. '
Which seems to indicate that you could search by name for William Morris.
I really though have no idea how one goes about researching at Kew, this is completely new to me. If you could tell me the kind of things you need to know, I'll do my best to find them out. I'm continuing my research all the time.