Hi Ian,
Tradition has it that a certain Aodh MacThormoid Morrison, a ship's captain from Lewis, married the daughter (or sister) of the Bishop of Caithness and, as her dowry, the couple were given land in Sutherland in the districts of Durness and Ashir. (the name Ashir has been corrupted and now appears on maps as Oldshore.) "Ay Morrison (or Morison) brought over from Lewis some 60 families of Morisons to settle on this land, and this is thought to be the source of many of the Morisons who lived and live stll in these districts. I have read several accounts of this tradition but none of them mentions any date.
To answer one of your questions: "Are the Morrisons and the MacLeods related", the short answer is: No, meaning they do not appear to have the same origins. With regard to the MacLeods, the origins of the eponymous Leod have been the subject of considerable debate but scholars do not agree. The Morrisons, according to the DNA study, in which I also participated, had over 200 sources of the name. From this I take it that the most common source is, as the name suggests, sons of Moore, Maurice (Moorish or dark complectioned) of which history records many, many.
All of that aside, the only reliable way to trace your 3 x great grandfather is to start with the oldest confirmed fact you have - a birth cert.; marriage cert.; or death cert.and work back from there, generation by generation. There are no reliable short cuts. Even family lore and family bibles should be confirmed.
Prior to 1855, there was no legal requirement to register births, marriage, or deaths. For most people, registration (mainly christenings & marriages) took place in the Church of Scotland Parish Registers. These were maintained by the Ministers and commenced at different dates by each parish, roughly from early to mid 18th century. If you Google, you can find out the names of all the parishes in the County of Sutherland and the dates that their register began. These registers have now been centralized and digitalized and can be accessed on the LDS site, FamilySearch.org, and on a pay-per-view site called "Scotlands People" ( I think, but you can find it by Googling - I don't use it myself)
Ian, this hobby requires a lot of time. Good luck!
IanB (morrison)