Time for another update, someone might find my troubles helpful in the future:
So I took the car to a lighting professional to assess the problem and talk about my options. He confirmed that the projector lens is damaged/foggy/dirty and is causing the poor lighting conditions and said that the best route would be to change the projector with a new one, without changing the whole headlights because the main headlight lens is pretty clear and undamaged, other than a bit of grayness. However, there are no new projectors for a H7 light fixture in stock, only for Xenons, so that option is a no-go for me as well. Luckily, the guy does a restoration service for such cases, where he takes apart the old projectors, re-chromes the interior, polishes and cleans the projector lens, and while they are at it the clean and polish the main headlight lenses inside and out and apply a protective ceramic coating to the outside lens as well. This whole deal will cost me around 150 EUR, which is half the price of a single new headlight, so it's an excellent deal for me.
I'll try and take several photos before and after, both aesthetically in the daytime and to show the light output at night, so that I can show the difference (hopefully). Updates will be posted in the next week or so.