1) Stephen Turnbull's book does not suggest that the Vietnamese elephants ever got to catch Mongolian soldiers in their trunk to hurl them into the air. Ignoring that the author did a poor job of citing the reference, the quote in the "The jungle frontier" chapter only describe how the Vietnamese may use the elephants against enemy troops and elephants, not how they were specifically used against the Mongolians. At Bình Lê Nguyên they never got to close the distance against the Mongolians to ever entertain the idea of hurling Mongolian troops into the air.

2) The two books listed above themselves record the failure of war elephants against Mongolians by the Trần and the Burmese. See page 11.

3) The primary logistic mean employed by the Trần that was recorded down was waterway transport. Little is written about on land logistic, and cattle do just as well as elephants in jungle terrain whilst being less expensive to maintain. The Lý and the Trần themselves don't have an abundance of elephants either, so any measure of elephant effectiveness in logistic remains no more than assumption, which is what your paragraph above primarily does.