Despite starting this thread, in the end I never did bother to attempt rooting.
Anyway, unfortunately now the phone refuses to boot. Not triggered by anything obvious, haven't installed any new software recently, etc. Just hung one day and then when I removed and re-inserted the battery, it won't get any further than the "docomo" splash screen. I.e. the OS doesn't appear to be getting bootstrapped at all. The "docomo" splash screen appears and disappears then the phone sits there with both screens powered up but blank.
As it happens, I had ADB Debug enabled in the developer options at the time, so I've tried to see if I can adb shell into the device, but no luck. Not surprised as it's clearly not getting far enough into the boot for that to work.
Any other suggestions? From the way it happened I do suspect it might just be hardware failure....
Not even sure how I enter recovery mode -- what are the key combinations for this?