As an update, my phone froze 3 minutes into Angry Birds, countering the 'games are ok' theory. It also freezes more than every other time I boot up after forcing it to power down from a previous freeze. Another strange action is that it often reboots when I try to power it off. Is that a feature and I'm just using the power button the wrong way, or is it failing to reboot?!

I suppose I can wait a week or so and see if any news comes along, after that I'll send it back. Fingers crossed it all works out.