I replaced the entire brake system on the 1973.Sounds to me like the booster is at fault. The booster used on the '73 Imperial is a "tandem" booster, meaning there are two big rubber diaphrams in it. Your description of the braking action having "two stages" makes me wonder if one of the diaphrams has ruptured -- thus, you're getting about half of the power assist that you should be getting, and you would loose assist as the pedal moves downward.
The car now resists stoping. It stops, but requires
almost double the pedal pressure and won't lock the
wheels unless both feet are on the pedal and really
jamming on it, and even then it's not that good a
response.
Also: when the brake is applied, the pedal feels
better in the top 40% of the swing until it seems to
"hit" something and gets stiffer - the braking action
seems to have two stages.