The plates just stop any lift, they don’t guide the carriage.

Are they like other Mini lathes with three cap head screws (no locknuts) and the two adjusting grub screws (with locknuts).

Not hard to thread a bit of 6mm bar to make your own studs or you can buy M6 studs off the shelf

Alternative is to use shim material to set the gap rather than the two jacking screws then you can tighten the three cap heads nice and tight.

Not sure what your 4 bits of metal are unless you are looking at the wiper felt covers.

The carriage is guided by the Vee on the bed and it’s matching vee groove. If your plates were loose then that allows the carriage to ramp up the vee when sideways pressure is applied and is likely the rocking you are getting. It also allows the tool to be pushed off the work as the rear or the carriage can lift.

The shere plates need adjusting so they don’t bind on the underside of the bed front and rear but allow the minimum amount of carriage lift. You will need to adjust them and then check the carriage moves freely along the whole length of the bed, adjust again etc.

No they just stop lift hence the screw adjusters work vertically. They do not guide the carriage, that is what the Vee does.

Have a look here about saddle adjustment. No mention of gap to sides of bed just underside of bed.

What Jason is saying is that if the saddle can lift.  It can ride up and down the Vee of the Prismatic bed, and be able to move to and fro across the bed.

If the lift is minimised by adjusting the bolts and gib screws, the saddle cannot lift, so it cannot move to and fro across the bed.

So tighten the bolts, and then adjust the gib screws to minimise lift, and the movement should then be reduced to an acceptable level.

Just as the LMS video shows.

Howard