The tall Besta comes with 4 metal scew clips that are used for the placement of 2 shelves you have to buy separately. The instructions show the Besta unit swaying from left to right without the use of these locking screw mounts and the use of shelves to create stability.
When you open the shelf wrapper it comes with 4 push in metal mounts. You dont use all 4 of those. You use 2 of the metal screw in mounts from the tall besta and screw them in the holes closest to the opening of the cabinet. Take the 2 Push in shelf mounts and place those in the back of the besta. You would repeat this for the second shelf installing 2 more Screw in metal mounts.
I was having the same issue with mine when using the Sidvik doors which weigh less than Glassvik. I only purchased one of the tall Bestas and it was going to be free standing without attachment to the wall. After following the directions the structure felt a Little better, but the cabinet still moved when I pushed it to the left, or to the right. I ended up taking back the single tall Besta and just keeping the double wide bestas.
I believe most collectors of statues here using the tall besta have screwed the units together which should take care of the swaying from left to right. I know You can also take your receipt to Ikea customer service and ask them to order you replacement cams, and they will have them shipped to your home. I have done this and they shipped me plastic ones no charge. I guess you can try to see if they will order you metal cams instead of plastic ones.