I’m working on a fix for the loose magnet issue since it happened to mine a few days ago. That said I need to test it and see how it holds up, but I think it’ll fix the problem. I have an extra frame, so I have no reservations trying to come up with fix for the problem.
It may be possible to realign the magnet. The way these are assembled is the magnet is only secured with double sided tape, which is prone to failure within ~18 months on the modern ones and typically years on older controllers. It is possible to fix it, but if you adjust the magnet and misalign it, you may never get it working right again; only do this if you can do it right. If it works but is loose, tacking it down with glue on the 1708 or glue and heatshrink on the 1537/1697 will keep the magnets in place again.
The problem you’re running into is either caused by the alignment of the magnet or the discrete components on the secondary board that are below the magnet that control LT and RT. The mechanism used my Microsoft doesn’t rely on carbon pads like the Sony controllers. I’ve posted a picture of the mechanism for you to see it:
Depending on if you are having issues with LT/RT or both, you will need to replace a few different components. The component marked 304 is the same on both sides, but the SMD caps and resistors vary based on which side needs repair. You will need to determine which ones you need for the side you are repairing.
The fix I put on my 1697 in 2018- and eventually 1708 has held up better than the analog sticks and Micro USB ports ever will on the 1697, and Micro USB on the 1708 (and long-term wear on the analog sticks). The fix for this is once it happens, cut the heat shrink (1537/1697 only - 1708-present do not need this as it’s clipped in), apply superglue to the magnets (anything good will work like Loctite or JB-Weld) and let it dry overnight so be prepared to be down a controller. Sorry, I don’t have another 1708 to show the patch work on beyond this answer as I do not stockpile previous models of Xbox One controller - especially the 1537. You also have no real way to remove super glue on these, as acetone wrecks plastic.