If you don't actually want to go to SIN and don't mind returning to Australia via the US from Europe, you might find it's substantially cheaper to buy this as an Australia / NZ - Europe return via the US. You can divide your itinerary into the following chunks and ticket them separately

- CBR-SYD-AKL (one-way)
- AKL-HNL-LAX-NYC-LAX-SYD (open-jaw Australia-US ticket)
- NYC-FLL (one-way, nonstop, cheap on eg JetBlue)
- MIA-LHR-NYC (open-jaw US-Europe ticket)
- point-to-point LHR-BCN and MAD-LHR (eg cheap one-ways on BA)
- a train trip BCN-MAD

You might be able to combine the Australia-US and US-Europe tickets into an Australia-Europe ticket via the US for further savings.

If you're only visiting the US and Europe and only traveling to major destinations like you are, the LONEx is almost never worth bothering with.