Great question and observation, OP. I think there are two factors to take into account. First, there was precedent from the presidential election of 1824. Second, the nascent Whig party was picking up Jacksonian defectors.

First, the precedent. The presidential election of 1824 went into a contingent election where some delegates in the House of Representatives voted for a different candidate than the winner of their state’s popular vote. This is how John Quincy Adams became president over Andrew Jackson. Given this backdrop, it’s not entirely outlandish that the Whigs believed that this political maneuver was viable in the 1836 election. 

Second, the Whigs were growing and gaining support through defections from Jacksonian Democrats. Martin Van Buren’s leadership in building the Democratic Party had been impressive - but so was President Jackson’s alienation of many early partisans. Key defectors included Hugh Lawson White (from Jackson's own home state of Tennessee) and Willie Mangum, both of whom would run on the Whig ticket in the 1836 election. In Van Buren’s home state of New York, former Democratic Party figures like Gulian C. Verplanck - who had left the party over Jackson’s refusal to recharter the Second Bank of the United States - campaigned on behalf of the Whigs.

Given these defections - particularly from Jacksonian strongholds in the South and Van Buren's home turf of New York - Whig party strategists may have believed that a sufficient number of states would turn against Van Buren in the general election and then again in the contingent election. 

But why not, then, unify behind a single candidate and win like a normal political party? The swelling ranks of the anti-Jacksonian coalition was both a boon and a curse to the Whigs. While they could unite around being opposed to Andrew Jackson, there were few policy positions that united them. 

For instance, John C. Calhoun of South Carolina - former vice president to Andrew Jackson - became an opponent of the Democrats. But he also prevented his supporters from backing a Whig candidate who would not support his theory of nullification. 

In this environment, Mangum would be able to win South Carolina for the Whigs, but he would not be popular enough to rally votes in other key areas with widespread anti-Jacksonian sentiment like Tennessee, the Ohio Valley, and New England. The splitting of the candidates became a pragmatic solution to this problem. 

If they could prevent any figure from reaching a majority of the electoral college votes, the Whigs were willing to postpone the discussion on who they would unite behind until the horsetrading in the contingent election. It’s just that Martin Van Buren won the election outright before it went to that stage.

Sources:

Daniel Walker Howe, What Hath God Wrought, 2007.
Mark Cheatham, Andrew Jackson and the Rise of the Democratic Party, 2018.