I think immigration is the best solution. There's no shortage of babies and young people in the world. The article notes that liberal immigration policies are not popular. Well, maybe that's the problem. I suspect that immigration will gain popularity when the problems caused by the ageing population become sufficiently severe. The problem will solve itself at the right time.
Surprisingly the process to get a work/student visa in Japan is much more easier than in Australia or the US (I've applied to one or another in all these countries and it's such a breeze to do in Japan).
Despite that, immigration remains low. For the foreigners here, last time I checked it was basically composed of about 80% of foreigners from China, 15% from Korea and the remaining 5% from the rest of the world.
I suppose the difficulty of the language and geographic location has something to do. Racism as known in the West is rare, but the truth is, Japan has consistently failed to assimilate any foreign population and it is really difficult to explain how it is like. I guess it's definitely more like a Canadian "cultural mosaic" more than an American "melting pot". But the cultural mosaic has some sense of equilibrium. For the case of Japan it would look more like "patching the kimono with pieces of fabrics of different patterns".
The thing is, under the hood, legally speaking, Japan is very open and welcoming to foreigners, but it fails to keep them in or assimilate them.