My Grandfather used to gather pine sap, for a turpentine company, just like the maple sap gathering, when he was a boy. He would carry a bunch of buckets, and spouts, auger. and a mallet, and long handled stick, with a chain, and ball with a hawks bill blade on it. He would swing the ball and cut a groove, in one direction, and then do the same in the other direction, making a " V " and pound the spout in the hole made with the auger, and hang the little pail on it, and go on to the next tree. As far as boiling stumps, sounds like a lot of work. But I would assume that they were boiling " Lighter " stumps. They make great firewood, and kingling sticks. Full of settled sap, and hard as a rock! You can dull a good axe real quick! But burns hot, and long!
You can cut a groove in a pine tree, and in a few days, you will have a sap ooze starting to build up. Just don't do it when the pine borers are infesting, like in the dry season. No point in helping the little $#@!!.
Besides there won't be much sap at all anyway, that is why the beetles do so well. We have had some pretty bad dry spells down here and the pine borers, are wrecking havoc. You can see acres, and acres of dead, and dying trees.
Wayne