I don't know if this is your family or not.
From the Manitoba Vital Stats site: http://web2.gov.mb.ca/cca/vital/Query.php
Their is a Michael Bachinsky who died at Brandon on August 19, 1914 at the age of 37 years. Man. Vital Stats. Reg. No. 1914-116030
(This was the only Bachinsky that I found.)
Under Bachinski their were four. but none match the names that you have posted however people some times have more than one name. Three of them died in the eastern region of the provience R. M. of Labroquerie, R. M. of St. Ann's, and Beausejour. The forth was in Brandon.
Vita and Stuartburn are both on the eastern side of the Red River Vita is in the R. M. of Stuartburn. Just north of the Manitoba / North Dakota Border. Their is also a R. M. of Franklin that is on the west side of the R. M. of Stuartburn. I'm not sure which municipality that the town of Stuartburn is in Stuartburn or Franklin.The town of Labroquerie and the R. M. of Labroquerie would be stright north of the town of Vita.The R. M. of St. Ann's is on the north side of the R. M. of Labroquerie, and Beasuejour is north still. All pretty much in a straight line.
The town of Franklin is in the Western part of the provience just north of the Yellowhead Hwy. # 16, between Neepawa and Minnedosa.
Hope this helps.