Actually I often filter as the OP did at the start. I think, and I know others agree, that filtering down the right if there is enough space, is considerably safer than filtering down the left. I can understand how it looks more dangerous with the traffic coming towards you, but, the fact that they have a clear view of you makes it safe from an oncoming traffic perspective.
By filtering down the right you also avoid passenger doors opening, parked car doors opening, Johnny driver deciding at the last minute to pull the car to the left to look closer at the nice pair of leather trousers in the shop window, left hooks etc. Of course you need to keep an eye out for cars doing u-turns etc, but you get a better view of what is happening ahead, and usually more space to react.
As with everything it needs to be done with care.