I had to send my N800 to Nokia UK for repair - they picked it up from my home address free of charge, which was nice - but it still took 5 weeks to be returned. The 1 month repair time isn't because it's being sent half way around the world, it's because the Nokia repair centre in the UK is bl00dy slow.

I'd send it to Nokia direct (have them pick it up!) and if they refuse to repair it remind them of their obligations under the Sale of Goods Act, mention having a word with your local Trading Standards office etc. - the WSOD is a known design fault, and as such it should be covered even outside of any warranty period.

If the repair center asks you for an IMEI number, quote your WiFi MAC address. When boxing up your 770, send only the device body and do NOT include the battery, battery cover, memory card, stylus or desk stand - keep these back as Nokia will not return them to you.