At BNA you are also up against the quality of the newsprint/OCR. There are two reports of this incident that I can see. In the one that I transcribed the OCR text has M'Kenzie while the other (has less detail so I didn't mention it) has "lil'Kenzie"
Saturday 08 March 1884
Glasgow Weekly Herald
AT KIRLINTILLOCH.— (bout nine o'c)ock on Saturday night travelling tinker name Isaac lil`Kenzie fell into the canal at Kirkintilloch, and was drowned.
search:
M'Kenzie: not found
McKenzie: not found
Kenzie: found
M*Kenzie: not found
Friday 07 March 1884
Galloway News and Kirkcudbrightshire Advertiser
About 9 p.m. On Saturday, while a family of travelling tinkers named M'Kenzie, consisting of father, mother, and several grown-up children, were going westwards along the canal bank at Kirkintilloch, the father, named Isaac, fell into the canal. The family were mach intoxicated as to be powerless as to render help, and though the alarm was raised, before the man could be rescued he was unconcions, and died in the policeoffice.
search
M'Kenzie: found
McKenzie: not found
Kenzie: found
M*Kenzie: found
Obviously this is a small sample, but maybe it's always worth trying the name without any prefix if all else fails?
