start and stop codons are not as clear cut as you're implying (there are often several start sites), and variable splicing adds a bunch more stochasticity.
There are also 6 potential open reading frames in any span of DNA. 3 phases and two directions. You're looking at it backwards though. The fact that there are options means the DNA can have the same meaning but a different electrochemical signature. It's a structural memory. It's both your genes and the necessary gradient to cause them to arrange in your chromosomes correctly.
I'm not here to represent the modern DNA research perspective. You seem to have adequate access to that already. I'm a programmer. If that means you must discount my point of view entirely then so be it.
You call it stochastic. I call it scaffolding.