Weird gyro effect while riding I have an old threaded headset and quill stem. Recently I overhauled the headset; replacing the bearing sleeves with loose bearings (filled to max and removed 1 bearing). The stem was also found to be too large to fit back in, and was replaced with a proper fitting one by a bicycle shop that specializes in older used bikes.

Now when I am riding I get this strange gyroscopic effect while riding (see this post for similar issue)

When riding in a straight line I can feel a push and pull to one side or the other, as if a ghost is steering my handlebars in millimeter amount, but enough to notice. It almost feels as if my headset is drunk, wobbling around in circles. A similar feeling would be turning your neck in circles as if stretching your neck... just not as intensely.

I've tried loosening the headset to the point where when I pick up the bike the handlebar smoothly drifts over to one side from the weight of the wheel being picked up.

Does it matter if the quill stem is tightened or loosened after the threaded headset is adjusted? I don't think it does.

I'm lost here! Please help!
The side to side you're feeling is that your headset is binding up. This can either be because it's too tight or because you've put some part of the headset in upside down (i.e. a bearing cage or installed the cups the wrong way around) or something is out of alignment. It is especially a problem on the bottom cup, when the headset is under load and can't micro-adjust the wheel as you ride.

Check everything is seated properly and in alignment (try putting a sheet of paper between the cups/races and the frame. Check all your bearings are clean and lubricated and nothing is installed backwards.

When tightening your headset you want it tight enough that there is no play, and no tighter. To check for play put the bike on the ground, hold the front brake and push/pull on the handlebars. Then do it with the wheel turned 90° left and right. Ensure you're not tightening the top race when tightening the lock nut.