I finally made it! Using a controller and getting three golds in two evenings is actually a great achievement for me, especially because yesterday I couldn't picture myself getting a bronze at Suzuka. In the end, I got a decent first lap and a good (I think silver-worthy) second lap there, and fortunately got a bronze there. I feel that, with a lot of work, I could MAYBE get to silver, but right now gold seems unachieveable without a wheel, at least for me.
However, if there is someone with a controller who's able to get gold on there, please do tell me, since knowing it can be done would motivate me to try it later on (right now, having the first X1, I'll just go on with A-Spec and B-Spec for a while).
Thanks for the suggestion of removing the ASM; I never use any help with any other car, but I felt those were "needed" for me to learn to drive the X1 at Suzuka and I thought I could get bronze with those. ASM off made the car a bit more fidget-y, which was great for the quick direction changes you have to make at Suzuka. I think it's precisely on those quick direction changes where you actually gain more with the wheel, since I know I am losing at least more than one second per lap in relation with the "gold videos" posted here, in the first sector.
Of course, I would improve more with a steering wheel pretty much everywhere, but especially on the first sector...
Now on to my humble advices for those who, like me, want to try getting a bronze with a controller.
I was VERY aggressive on the first corner, I accelerated until very late and braked while turning in, although not too much, in order not to "kill" the momentum. Then trying your best to find a fluent pace through the esses, not trying too hard since you might go wide. Degner #1 is almost flat out, I just left the throttle a little bit. I suppose it's a matter of "balls" there. Degner #2 is actually breaking early and accelerating over the inside kerb. The following corner I found it to be quite tricky sometimes; you have to break late but HAVE to hit the apex, too, otherwise you end up losing too much time. Then, on Spoon, breaking late on the first corner and very late on the second, which places you in a good position for the backstraight. I never found a comfortable way of facing the Casio Chicane, but I wasn't too slow either, so... that was it! 2:15:7 or something like this, I got