My observation of Japanese knotweed in eastern Canada, where it is invasive on disturbed land, is that is does not invade dense mature forest. It grows up to the edge of the forest but not beyond, and this must be due to it being intolerant of shade. In open conditions it is very hard to remove. For this reason, I think shade is the answer.
Shading could be enhanced by selecting trees which create toxic soils (such as walnut [Juglans] and hemlock [Tsuga]), though this would create a subsidiary problem of course.
It should be noted that forests are commonly dense and evergreen in eastern Canada, more so than the relatively open deciduous forests of Europe, and so the shading effect is particularly strong here. This may need to be considered when using the shading tactic in Europe.
By the way, deer nibble away at knotweed in Spring, so this also helps the forest-edge effect (albeit with its own suite of disadvantages).
European? Hmm, good question, should think about! But how bout Japanese vs. Japanese ... try bamboo ... would drive out the bad with the worse, I guess ! But would give a better appearance, ... and then you could harvest the bamboo, at least ... not much you can do with the knotweed, right!?
Knotweed is a major source of resveritol, a dietary supplement thought to have excellent health benefits. It is the compound found in red wine that is supposed to be beneficial in the "Mediterranean diet." It might be harvested with profit, but it must be refined and another compound that produces diarrhea removed from the resveritol.
After what I have read, I would not recommend planting other species until you have eradicated the Japanese knotweed properly. Planting shrubs or trees may inhibit further control efforts and reduce control options against knotweed regrowth (Child and wade, 2000: "Japanese knotweed manual"). This can make the eradication process more costly and difficult than necessary. Alternatively, you could sow grass species for active revegetation. This will enable monitoring of knotweed regrowth and you can still use mowing (or even spotspray, perhaps with a selective herbicide) to control regrowth. Although knotweed thrives best in full sunlight and competition may affect growth negatively, the knotweed can escape competition by spreading laterally through rhizome growth. Be aware that it is reported that knotweed stands can stop shoot production for three years after being treated with herbicide, and then start producing new shoots (Soll et al. 2008: "Sandy River Riparian Habitat Protection Project Report 2008."). Digging of soil surface may stimulate dormant buds to sprout. Digging of soil surface and fragmentation of the rhizome system also increase shoot production in general, which can increase the efficiency of manual removal, if manual removal means handpulling or cutting.