I'm guessing it is your rear brakes that lock up first. That's normal for a factory Mopar brake system. If it is your front discs, you have something else going on at he booster/master cylinder as mentioned above. A larger bore master cylinder will reduce the rate or slope of the initial brake pressure, a smaller bore will steepen the rate of pressure increase.

As mentioned above, the master cylinder rod adjustment is critical. Its a bit of a pain to take it out and adjust it, but the time doing so is well spent. This era of Mopars tend to lock up the rear brakes way to early, especially on a panic stop. Drum brakes are "self-energizing" by design when applied. The brake shoes on them essentially wedge towards the brake drum once they start touching it and that wedging effect increases the total force of the braking at a given wheel.. Adjusting them does help significantly, but there are other "tricks" to reduce the overall braking power the provide once applied such as changing the wheel cylinder bore size, removing a portion of the brake pad(not too much though) and using either a proportioning valve or pressure surge flattening device.

On the surface, It sounds to me like you need a larger bore master cylinder. You can contact Dr Diff to find out which one you can swap out to reduce the rate of braking for a given pedal pressure.
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1970 Plymouth 'Cuda #'s 440-6(block in storage)currently 493" 6 pack, Shaker, 5 speed Passon, 4.10's
1968 Plymouth Barracuda Convertible 408 Magnum EFI with 4 speed automatic overdrive, 3800 stall lock-up converter and 4.30's (closest thing to an automatic 5 speed going)