Sounds like they were trying to time the brake and either didn’t cut the shoulder back far enough to use shims and/or botched the size of the brake and just decided to torque it on until it lined up. Definitely not the right way to do it.
Pictures and a timeline of what was changed (with accuracy at each point) might be helpful. If we know it was shooting 4” groups with a gritty trigger, and then 10-12” groups after you pulled the barrel, it’s a good bet that the issues were caused when the barrel was pulled.
To be honest if you pulled the barrel, stripped it, and put it on a lathe, you introduced a whole bunch of variables for potential errors beyond the standard question of “how do I improve accuracy”. At this point, I’d just say that the barrel was screwed and start over. Any errors are probably at the muzzle, so I’d put it in the lathe, ensure it was correctly trued, and then part off the barrel behind all the previous work and start from scratch with a new crown and threads.
Be very careful and exact in your measurements, and use a good thread spec when you’re cutting your threads. Things like the specific size of the threads, shoulder, and undercut should be in there. Here’s one example from TBAC, and there are some other good ones out there as well.
https://thunderbeastarms.com/tech/thread-specifications
Good tools are invaluable as well. I’d recommend getting good indicating rods, and making sure your indicators and spider are up to the task.
Outside of that, I’d just get another barrel and chalk it up to a learning experience. After that, I’d reassemble everything making sure I was doing it correctly. I’d probably recommend swapping the handguard to a good/known brand if you think the current one might be causing issues, but I wouldn’t expect a handguard alone to cause a 10-12” group.
Other things to look for if you’re able to use a lathe to accuratize an AR might be cleaning up the threads on the receiver and squaring the face, and essentially all the other stuff you’d do to blueprint a bolt action. If you really want to go down that rabbit hole, you can also look at the chamber and the barrel threads/barrel extension line up. Just be aware that headspace is set by the barrel extension, and any changes there will likely affect barrel timing which means your gas port may not be vertical anymore. But if you’re going that far, you might as well start with a barrel blank.