How to fix a metallic bicycle basket to the back rack?
I would look at 3~5 small aluminium fish plates in the basket, and small saddle clamps under the rails.  You'd need two small stainless steel bolts and nylock nuts per plate, or some other way to reduce vibration.

Suggesting Stainless Steel to avoid rust, or you could just use grease.  This will make undoing the bolts hard later, and rust may mark things you put in the basket, like cloth.

This suggestion would not be easier, but it will be a lot more durable.

There are metal zip ties, but they will have the same loosening problem, which is exacerbated by the small radius they have to clamp around.

Some ideas:



Imagine the above but with the bow replaced by 

and some bolts with the threads facing downward.
You could use old spokes or other metal wire.  Spokes are hard to bent with fingers so pliers might be required.  Any sharp end could poke a hole into load items in the basket too.  I've got a box of thousands of galvanised concrete reinforcing tiedown wires that can be bent by hand.