If you are happy with the shape but only want to soften the leather, use more Proofhide, top and bottom. I usually put the Proofhide on the leather, put the saddle in a closed plastic bag and set it in the sun for a while. The heat from the sun helps warm the saddle enough that the Proofhide can soak into the leather quite well. I live in an area where it almost never exceeds 90 degrees F (32 degrees C), but putting it in the plastic bag allows more heat to accumulate and liquify the Proofhide without being excessively hot to damage the leather.
I use the Conquest model, that is sprung like the Flyer. I like it for smoothing out some of the road vibration, but the extra steel adds weight. The springs deflect maybe about 5mm when I sit on the saddle, not enough to notice and certainly not enough to cushion big bumps. But it gets rid of some of the rough road feeling. But if you are using wide tires, the springs might not help much as the wider tires would serve the same purpose.
Also if you are a lighter rider, the springs might be too stiff to help much. I weigh about 175 pounds (about 80kg).
When I try to break in a new Brooks, I pull the seatpost with saddle attached out of the frame and soak the saddle in cold water for about 15 to 30 seconds. Put the seatpost back into the frame and ride the bike for a short ride, staying near home. (The reason that I stay near home is that if I find that the leather is deforming too fast, I want to get off the saddle right away and stay off it until dry.) If that did not do enough, try it again and maybe increase the moisture level in the leather by soaking it for a bit longer. Once I get the shape most of the way I want it, then I apply Proofhide. Proofhide seems to give the leather an ability to resist taking a new shape, thus I do not apply it until I have the leather shape where I want it.
It is easy to get overly enthusiastic and get the leather too wet, resist that urge. The goal is to get it moist, but not wet. I usually soak the leather three or four times before I get the saddle where I want it, I would rather spend more time repeating the soaking than risk damaging the saddle by getting it too wet.
The surface of the leather has sometimes lost some of the smoothness in the sitbone areas where the leather deformed the most, but that has not been any problem for me.