Gallows Street does become Milebush Road. Originally this was the main road from Hillsborough. Later the road entering via Princes' St became the A1. It has been superseded by a dual carriageway by-pass which cuts across Milebush Road. The Milebush Road re-joins the dual carriageway about 2 miles out of Dromore . The Magherabeg Road joins the Milebush Road from the left about 1/4 mile short of this junction.
Much of the land in this area belonged to the Hill family but I'm not sure about Magherabeg. My father once pointed out a boundary marker on a road which joins the Magherabeg Road near what used to be Magherabeg School so I think it may be just outside the Downshire Estate. I have an impression I once saw a map which designated it as 'Church' land ie owned by the Church of Ireland. I'll try to track this down again.
The big estates were bought over by the government at the start of the 20th century and sold to the tenants by Land Purchase Annuities which were effectively very long (66-year) mortgages at fixed interest. Tenants could sell the land and the new owner took over payment of the LPA. Most of these LPA's came to an end from the 1960's onwards. I'm not sure about Church land but I think there was a similar arrangement linked with dis-establishment. This would explain why your great-grandfather could buy the property from his father's estate but previous generations were tenants.
One online resource I can suggest is the Public Records site
http://www.proni.gov.uk If you select Ulster Covenant then Search and enter Name, Morrison; Parliamentary Division, Down:West; & District, Dromore you will find there are two for Magherabeg (or Marabeg) Hugh and Margaret . You can display and print off the pages with their signatures. This was in 1912, so it is probably the Hugh Morrison you are looking for.