I have had another look at what was written in the first place and the references that cropped up in the subsequent discussion. As you will gather, the timings left records unlikely to help so I have not found anything fresh to guide your search. However, I am pretty sure we did identify some relevant locations. The most specific is the Island of Flodda off the northeast coast of Benbecula but connected these days by a causeway; it is certainly the site identified on page 848 in the Appendix to Fr MacMillan's book To the Hill of Boisdale. There are only and at most have only ever been six holdings on the island. Apart possibly from No.4, all were at the relevant time in the hands of one extended family, descendants of an Angus MacDonald a descendant of Ranald MacDonald I of Benbecula who died in 1636. Pretty well all the descendants who had the tenancies married wives from North Uist. A couple had descendants who, as mentioned by Fr MacMillan, emigrated to Cape Breton in the 1840s and to Saskatchewan in 1883/4. The most likely to be closely related to you [though this is may speculation] seems to have been the family of James MacDonald at 6 Eilean Floddaigh. The lands that went with that holding seem to have been absorbed into 4 Flodda at some point but there is a small house on the shoreline, accessed by a drive along the beach, that probably represents the site of the original dwelling. Do have a chat to the locals as it is amazing how much of ancient history is preserved in tradition.
On the assumption that the tradition is correct that Alexander settled for some time at Nunton [Baile nan Cailleach, the town of the nuns so not Caiileach alone], he will not have had a lease/tenancy. At the time Nunton was the home farm for the estate and from 1797 was the residence of the Factor or Estate Manager until the 1840s, when it was let out as a commercial farm, this persisting until after WW1. Accordingly, Alexander and family will have lived in the little cottar settlement on the moor to the east of the main house. It is no longer there except as traces of dwellings. His daily work will have seen him in and around Nunton Steadings, which is across the road from Nunton House itself. The house and surroundings are little changed from the early 1800s.
The Island of Grimsay [beware because there is another off the east coast of Benbecula] lies in the Sound between Benbecula and North Uist. Again it is not exactly extensive and you can drive round it in a quarter of an hour or so but, in this case, there is no indication of where the connection may have been. Carinish is then the first settlement on North Uist itself and indeed the references to this location may have been an approximation for Grimsay.
