I took out a big honey locust tree with a boom lift like that (well, it was partially cut through). Just put the forks against it about 15 feet up, and drove forward. Took me three hours to stop giggling, and Dad had to grab the lift keys out of my hands to keep the rest of his trees.
BTW for a smaller stump, just burn them out when it hasn't been raining for a while. Drill a bunch of big holes in it, then charcoal and a little gas to get it going. Had charcoal as necessary, you shouldn't have to use more than a half bag to get it 2 inches below ground level if you cut it off close to the ground.