Daisy-chaining regulators is a bad idea. They can do unpredictable things.
I just helped a teen track down an issue with his science fair project. His board was blowing a somewhat expensive ADC during powerup about 1 out of 4 times.
The schematic showed several linear regulators daisy-chained as you are trying to do. At one point, a mid-point regulator supply 12V dropped low as several regulators downstream of it asked for more power as their circuits came online. But the 5V lines didn't drop, this was causing some ICs to have voltages at input pins while their power supply pins were too low, sometimes blowing the ADC.
I've seen that kind of thing before, although it often just causes everything to powerup in some odd state rather than blowing ICs.