[DavidG]

The two controls (pedal and hand brake) are independent of one another. If all four wheels are adjusted properly and all four brake rods are adjusted to the correct position of the arms on the brake cross shaft on the center cross member, you can adjust your brake pedal to raise it for earlier engagement of the brakes. However, your hand brake issue suggests that at least some, if not all of the problem arises from incorrect adjustment of the system before the brake pedal enters the equation.

Are your brake drums still within the allowable maximum inside diameter? There's an easy way to tell by looking at the arms attached to the external front brake operating shafts and the arms on the rear brake backing plates. At rest after adjustment of each wheel's brakes those arms must not be anything less than vertical toward the center of the car. Better yet is when they are slightly off vertical toward the front of the car for the front brakes and toward the rear of the car for the rear brakes. That ensures the maximum amount of leverage and the smallest amount of movement of the brake rods and ultimately the brake pedal for the brakes to perform as intended. The next step is covered in the following paragraph.

When the hand brake is off and the system is at rest are the arms on the cross shaft that the brake rods attach to in a vertical position or slightly beyond vertical towards the wheels as they should be when you adjusted the rods (after first adjusting each wheel's brakes)?

Do not adjust the pedal until after you've taken the above steps progressively. It may require little or no adjustment.

In addition to KiWinUS's helpful addition, all of the above assumes that all the clevises and clevis pins are not excessively worn nor are the holes for the clevis pins in the ends of the brake rods and operating levers oblong out of round. If any of these are worn, replace them. NOS brake rods are becoming difficult to find and you may have to weld up the holes and drill new holes of the original diameter.