I think the clue lies in the "long taxi". You're quite right that the double bing advises the crew the aeroplane is entering the live runway and tells them to get strapped into their seats.
However, the pilot in charge of the sector will have briefed the crew thus "I'll sound a double chime when we enter the runway and you need to bucke up at that point." It may well be that on the briefing of your flight, the pilot had told them "We have a bit of a wait before pushback, so get your safety demo out of the way and your cabin checks done and then strap in. We have a long taxi, so we won't need to sound the chimes."