OK, so after chatting with Swiss Air yesterday, I've sent the receipt to them again.
They approved my claim at 7 this morning and said I could get my money back as a refund or as a voucher.

I was wondering if they'd be willing to consider a slightly higher voucher amount if I asked? To be honest, I don't think the offer's a bad deal, especially since I'm planning to book a flight with Swiss Air soon.

They offered me either £350 in cash or a £500 voucher, based on the amount I actually spent.

Everything is relative, but I thought Swiss Air's service was way better than Lufthansa's HON Centre. I asked the HON helpline for an update a few days ago, but they just told me to ask Swiss.

If I hadn’t asked the Swiss, I don’t think I would have received the money…