The difficulty of removing scratches in transparent acrylic is to avoid
creating another optical/aesthetic flaw to cope with.

Some things to consider:
Buffing wheels can quickly heat the acrylic to softening and discoloring.
Polishing compounds that contain petroleum-based solvents can damage the
acrylic.
Polishing compounds designed for plexiglas are safe but are often fairly
expensive.

The best method IMHO involves using a series of successively finer grits of
a highgrade water based polishing compound for automobiles.  In the United
States, there is  brand line, Meguires, who sell an excellent line of
polishing compounds for collector cars.  Though these are expensive car
polishing liquids they are  cheaper than the standard plexi polish.  I
suspect there are similar products in Australia.

If you are working on a deep scratch you will want to start with a coarser
compound and work over as small an area surrounding the scratch as
possible. Polish just until you can no longer distinguish the original
scratch from what will become a slightly opaque or fogged surround (an
evenly "scratched" texture from the grit).

Be sure you minimize the amount you are polishing away by frequent checking
(blot and rinse off the area).  Once you have "erased" the scratch you can
deal with repolishing the plex back to full transparency by moving to
successively finer grits until you recreate the glass-like shiny surface of
the original plex.    Be sure to use a new cloth or rag each time you go to
a finer grit.

If you try to do the whole thing with single grade of fine grit polish it
will take a LOT longer and you risk creating a wavy surface that will be
noticeable visually.

Claire Pillsbury