Is that mounted to the side of your bench? It looks like you’re going to tear it loose every time you pull the handle.
I use @Cowcatcher mounts. I can assure you they aren't getting ripped off the bench. Here is where I built my table. Its same principle as a 2in receiver hitch with steel plates so you can move presses around. That mount has a lee quick change installed on it and the press has a lee quick change plate. So I move my Lee Single state, trimmer, Dillon Swager and other items in and out of that mount. Its really not flexing that much its just the shell tube wobbling around gives its that look.
Here is just base while running. This press is not as solid a single stage just the way its made. So it does have a bit of slack in it.
Edit: After looking back at videos I see what you are saying the swaging video is flexing it pretty good. Never have put that kinda torque on it with my single stage or my 550. Never noticed that before. I had the top held on with just 4 screws in the corners. I added a couple to the sides of the mount to add more stability they seems to have help with flexing under the load of swaging.