Is a Kasich Knockout Even Feasible?

The John Kasich campaign is bargaining on winning the hearts of minds of delegates committed to vote, in the first round, for Donald Trump and Ted Cruz, in spite of the fact that he currently has fewer delegates to his name than Marco Rubio, who dropped out weeks ago after losing his home state of Florida to Donald Trump.

In defense of their strategy, they cite other contested Republican conventions in which the candidate with a plurality of the delegates going into the convention did not emerge the winner.

In particular, the Kasich campaign cites two: the 1860 nomination of Abraham Lincoln and the 1952 nomination of Dwight Eisenhower.

However, in both cases the ultimate winner went into the convention in second place in the delegate count.

For example here were the results from 1860:

Source: https://en.wikipedia.org/wiki/1860_Republican_National_Convention

As you can see, Abraham Lincoln went in with a high number of delegates, well ahead of the third place contender.

Similarly, in 1952 Eisenhower went into the convention nearly neck-and-neck with his rival, Ohio Senator Robert A. Taft.

Therefore, I have a hard time envisioning a scenario where the nomination does not go to Donald Trump or Ted Cruz and I am not sure, as much as I hate to admit it, what John Kasich is still doing in the race.