You're right that it's rarer, though it's hard to put exact numbers on these things. The distances and amount of hostile territory to cover make things far more difficult. There's a great deal of stealing oneself in the Lower South, but it's usually more in the vein of getting a break from the horrors, seeing distant loved ones, and so forth than planned, permanent escape from slavery. Slaves fleeing to the North or Canada is largely a border state concern which the Lower South presses out of slaveholder solidarity rather than one that they understand as a direct threat to themselves.

But if one was a slave and wanted to get out of the Cotton Kingdom, then options existed. The most reliable ways would involve riverboats or coasting vessels. In the Mississippi valley, the steamboat traffic ran so fast and heavy that it became a known route for escape. Everyone is on a schedule and trying to stay ahead of it while piling on as much cargo and passengers as one can. The boats themselves are often thrown together affairs intended to last a few years at most, powered by inefficient, but cheaper, steam engines which are also more prone to explosion and often have safety mechanisms absent or purposely disabled by their engineers. It's an unstable environment where a lot of people don't care or turn a blind eye. Nightly stops for fuel and routes that go up into the North combine with all that to make probably the easiest way to get out. Of course boats are still small places and the telegraph can outpace the fastest one, so people get caught by suspicious passengers or crew or pulled off at a landing a day or two, sometimes more, up the line.

In Alabama, one could get into the Mississippi valley system by means of the Tennessee. Failing that, as geography may dictate, an enslaved person might escape by getting down by Mobile and catching a ship plying the coastal trade. There could take one to New Orleans and back up the Mississippi, but it's probably more likely one would catch a ship taking cotton to Europe by way of New York or Baltimore. Get on and stay on for the whole time and you're out.

William and Ellen Craft fled from Georgia essentially that way, through with a few departures. Ellen could pass as a young white man, so she posed as William's owner going North for his health. They got a ship up to Virginia and took the railroad from Petersburg to Pennsylvania, where a few young ladies took quite an interest in the fetching gentleman sharing a compartment with them. Ellen had a standing invitation to call at their plantation when she came back through Virginia. The Crafts were relatively well-known in antislavery circles at the time, going on the lecture circuit to large New England audiences, but their careers as activists took a turn after the Fugitive Slave Act passed. Their enslaver sent men to take them, so the Crafts fled Boston for freedom and safety in Britain.