You've certainly gone to some extremes to check this out, but your investigations should give you a good clue that the problem is with front axle. So, it could either be the differential that is clattering and making the car judder or, perhaps more likely, the front CV joints which allow the car to drive its front axle while also steering the vehicle. Once you take the load off the front driveshafts (by disconnecting them) the noise stops because the worn CV joints aren't taking the strain of trying to move the car, so they don't make the horrible noise. In some cases, you can simply replace the worn out CV joints, but there's also the option of complete driveshafts (with new CV joints already fitted) that are a simpler fix if a bit more costly. You can also buy driveshafts new or reconditioned. Its sounds like you're more than skilled enough to tackle this at home.