Shoot! I didn't do the top/bottom I did side to side, but I did 'lock' the steering wheel before doing it. I'll try again tonight, but doing the top/bottom.

 

Also lift just one wheel at a time. If both are off the ground they can both swing from side to side by moving through the steering rack. Even with the wheel locked it will still move slightly.

 

Check these, my 2001 chatters hard like the freeway is wash boarded if I hit a bump during a shift then clears up under power. Your car is low miles- but if drivein hard like mine you clould have done what I have done and blown these out of the control arms:
Replacing 01-05 Honda Civic Front Lower Control Arm Bushings - YouTube

 

Lifted one wheel at a time, and there was zero play (up and down) when I tried to move it.

jrm,
My 92' must be different because the part that you show moving up and down in your video, I don't think I have that. While it was jacked up I took a light under there and looked for it.