I think Japan stopped growing rapidly partly because they'd caught up with the west and couldn't keep transforming by copying more developed countries. I don't think China's there yet. Maybe if their gdp/capita goes from $6.8k (China) to $39k (Japan) that will be the case but there's a way to go.
The problem is more that the rest of the world cannot absorb more chinese exports, which force the chinese to have to do consumption based growth. Changing direction of growth like that is not simple.
Not only is changing direction extremely difficult, service based growth is far slower compared to manufacturing based export growth when you're coming up from nothing as China did, starting from $300 GDP per capita in 1990. They were able to tap into virgin (to them) export markets in the US and Europe. As you noted, there are no more well-off consumers to provide for their export growth, that party ended in 2009 or so.
The problem here is China has seriously miscalculated and focused too heavily on exports. The rest of the world doesn't want more Chinese exports than they did in 2007. Export lead growth only gets you so far.
Japan [with a population of ~128 million] could run its economy into exports and scale to catching up with the West in that manner because of the smaller population.
China's exports have stopped growing and that is a very, very serious problem with debt fueled growth focused on exports. They'll have to print money [to bring export growth back and avoid a private debt bubble bursting] which is why everyone is betting against their currency. Or they'll go into a recession and they'll need to print money.
That said, plain old GDP also matters depending who you are. If your country's economy heavily relies on Chinese imports/exports (see my other comment), your government doesn't care much about the average Chinese citizen's living standards.
