Best way to polish an LTR..  

I wasn't aware that you...
I wasn't aware that you could remove scratches in this type of material.

I don't mean remove the deep...
I don't mean remove the deep ones, just the surface scratching really - doesn't look like it has actually gone past anything but the lacquer maybe.

You could try
Filling them in with a scratch remover.

Try
clear lacquer nail polish. I have a Diamond & Baratta high lacquer coffee table with a couple of dings in it along the edges. It is a deep cerulean blue. I used a blue magic marker to color the spots and filled up the dent with nail polish and it is indistinguishable from the original unless you are right on top of it.

Would
removing some of the minor scratches (if it could be done) and leaving the major ones, really improve the appearance of your table ?
Unfortunately, plastic laminate is virtually impossible to repair -- like touching up a scratch in a metallic silver auto fender. You have to replace the piece of material. When there is an open seam between adjacent pieces of Formica, SeamFil can be mixed to a matching color and will help make the seam disappear. But there isn't anything that I know of -- including lacquer -- that will bond for long to the face of laminate, either to the clear surface melamine layer or to the resin-impregnated paper immediately below that.
Polishing the melamine is useless; the only result is a change in sheen, which produces another noticeable defect. And any scratches through the clear melamine layer will not be removed by polishing.
Sorry to be the bearer of bad news. . .

Brasso works well on a lot...
Brasso works well on a lot of plastics for removing 'haze' type small scratches