What I've done in the past is to use a drill, locking the chuck directly onto the stripped screw or bolt. You need to make sure there's enough room for the chuck and drill to do this straight on, and make sure the chuck is tightened to the absolute max that you can. (I've tightened the chuck hard enough to deform screwheads/threads to make this work.) If you don't have this straight onto the bolt/screw, you can get some really nasty extra motions involved which can cause damage to you, the drill, or other items in the way of the drill.
FYI, you'll need to remove most of the JB Weld to make this work, but that'll mostly happen naturally as you crank down on the chuck. Just make sure to remove the chunks of JB weld from the chuck before you start extraction. You don't want any debris in there that could prevent you from getting the contact required for this to work.
If your drill spins on the bolt, but the bolt doesn't move, you don't have it on tight enough. This might even cause your chuck to slip off, which is a bit dangerous on it's own. You might have to use the edge shaping options some of the other Answers talk about. The difference between using this option and using a socket on the edge shapes is that this puts a lot of pressure to clamp onto the bolt that the socket just doesn't do. This ends up being a combination of using a locking plier and a socket. However, with the 3 jaws in the chuck, you'll get a way better grip than the locking plier. (BTW, a locking plier can all too easily slip off the bolt, even if you do shape the sides.)
As well as spinning on the bolt, you may end up breaking the screw/bolt. This is usually more of a concern with small screws, but it can happen, so it needs to be said.
Doing this can be a bit dangerous, so take it cautiously, but if you apply power slowly, it can work when all else fails. You need to make sure you have an absolutely firm and solid grip when doing this, as you are putting your force against the whole of everything the bolt/screw is stuck against. In your case, you can butt the drill handle/grip up against the pipe so it takes the force, instead of your wrist. With the pipe, unless you hold the drill solidly, you risk slamming your hand into pipe as well as wrenching your wrist badly. I've heard of people breaking their wrist using a drill normally, and this definitely has more force involved than most drilling applications.
I recommend using a corded drill, as they tend to have more torque available than a cordless*. However, if you have a pro series/brand &/or impact cordless and a tiny cheap corded drill, your cordless might end up having more power.
Note: This requires a variable speed and reversible drill. I doubt that non-variable speed or single direction drills exist anymore, except as rare pieces of antiquity, but I thought it needs to be said.
* I base this on the fact that I've used a 10 yr old 1/2 hp corded drill (with a keyed chuck) to easily get out a screw that a 20v Dewalt and 3-4 other cordless drills couldn't budge.