I've gone back to trying the 'triple button press'. Two presses without the brake pedal pressed down to switch on the ignition. Then wait for several seconds. Then start.
It still doesn't start immediately at 1,500 rpm but it's no longer so obviously starting slow and it's fractions of a second before it picks up to 1,500 rpm. Last night was slightly more interesting. Totally new behaviour.
I was expecting it to be a useful test because it was a warm, wet evening and similar conditions to the one and only time it's ever not started first time from the office car park. What it actually did was spend a couple of seconds spinning the starter motor before roaring into life at 1,500 rpm. It never normally runs the starter for more than half a second.
So I don't know what to make of that. Sadly without a time machine there's no way of knowing what it would have done if I'd started it as Honda intend. It's suggesting however that the problem isn't directly temperature related. I'd say it was related to absolute humidity (relative humidity conflicts with it being happier during summer).