Where I live, Mitre 10 has free dropoff of polystyrene for recycling.

There's a list of dropoff places on this page: https://www.expol.co.nz/recycling-programmes

The list seems to only have Auckland and South Island stores, I'm in neither and my local takes polystyrene so definitely check in with your local store.

It notes that they can't do large volume, only up to 2 rubbish bags full equivalent at a time, so you may have to drip feed it in.

And as an aside I've noticed a lot less polystyrene in appliances these days if you get more expensive brands.