Answer: The proponent of South-East as the direction of Qibla from North America are giving only the argument that North American continent is North of Makkah and West of Makkah, therefore, Qibla should be opposite to that meaning South-East. This is all due to flat map, latitude & longitude lines, and preconceived idea that Makkah is somewhere down from Northern latitudes.
Makkah is at a longitude little less than 40° East. Now, ask yourself about Qibla from any place in Alaska (approximately 140 West longitude or more), and the Qibla from Yukon Territory of Canada (less than 139° West longitude). By the flat map theory, the answer for Alaska would be South-West and the answer for Yukon would be South-East. Does that make sense, for two places adjacent to each other. If one is impartial from the preconceived notion mentioned above, one must think it rationally. It doesn't make any sense to me!
The idea of a minaret over Ka'bah is simple, that the sun comes over Makkah on May 28, and July 16 every year around local civil noon time (not exactly at 12:00 noon). Noon time is defined as the time when the sun is at its highest point in its journey from sunrise to sunset. The sun shining at exactly over Makkah makes an imaginary minaret over Ka'bah. Looking at that sun from anywhere on the globe is the correct direction of Qibla. Only two things are needed to verify this.
1. Either go to Makkah on those two dates or ask someone in Makkah on those two dates to verify that the sun comes over Ka'bah at 12:18pm on May 28, and at 12:27pm on July 16.
2. Go to Nova Scotia or ask someone there on those two dates to see the sun at those times, and check the direction.
If you do those two things, there would be no controversy.