Escort ZX2 brake problem

After a close call yesterday, I decided to see if anyone knows anything about the brakes in a ZX2.
The problem I have with the brakes is that they are weak. When I
really slam on the brakes, they get to a point that feels like the maximum physical extent of their travel before the tires will lock up, almost like there is a physical stop to the brake pedal or linkage that prevents additional pressure to the pedal from translating to additional braking force. I've also wondered if there is some front/rear bias issue that bottoms the rears in a way that prevents the fronts from getting any further pressure to the calipers. At first I attributed the problem to simply mediocre brakes as a side effect of rear drums but I'm not so sure.
The car has relatively sticky tires on it compared to the OEMs but I had the problem before the tire upgrade. I could only lock the tires on wet pavement.
Any ideas or explanations?
The brake pedal will not go to the floor, it does not seem spongy or to have excessive travel, and it does not seem to improve after pumping them.
The car does not have ABS.
Thanks for any suggestions.
JP
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