96 jumps left then right when applying brakes

My 1996 Tahoe 2 wheel drive 4 door with vortec 5.7 and 393,000 miles has been a faithful ride requiring just 6 fuel pumps and one transmission. I bought it 7 years ago with only 40,000 miles and from day one the brakes seemed soft and spongy. I attributed this to the 18 inch wheels and tires and learned to live with it, waking up many nights in a cold sweat as I mashed down harder and harder on the brake to keep from hitting that car ahead of me. I keep up on maintenance oil change lube ect. And do all the work myself but I've run into a problem with the braking system thats got me baffled. When applying the brakes the left wheel grabs and pulls the truck about a foot to the left then the right side grabs and pulls the truck back to the right 2 foot or more. Even cold and at low speeds you can see the steering when jerk left then back right. When I heat everything up its worse. I've replaced calipers pads and rotors and a new master cylinder last year dumped the 18 inch wheels and tires for a 31X10.50X15 combination. The 18 in tires had 75,000 + miles and were in good shape save for the right front and it was worn beyond service on the out side edge with the wear indicators still below the tread level across the rest of the tire. The abs (4 wheel) light is not on and it shows no codes. What am I overlooking?