What about the possibility that a single section of DNA could directly encode a number, rather than that number be only indirectly determined through the outcome of a multi-step process, specified by multiple genes? (which I agree is the norm)
The only example that I am aware of like this is the telemeres at the end of DNA strands. However, although they do directly quantify the number of times the DNA can be replicated as encoded in their length, the resulting trait of lifespan is obviously affected by many other factors.
Is it possible that some other regulatory genetic sequences operate like this, encoding a number in the length of the sequence?
All in all, I agree with your description of how resulting physical traits take on a continuous spread of values through a mixture of accident and complexity. And in the absence of enviromental differences, each trait is determined from the DNA through a process that can be unique to that subsystem that exhibits it. So in that sense, there are a dense jungle of different types of pathways that map the DNA to the numeric values of our traits.
I also gather from your description that most of the information in the network of genes that help to determine a trait, is ultimately stored in binary form. With a sufficient number of these genetic bits, a continuum of values can be well approximated. It is just how that information maps into a trait, which is what varies from system to system.
It is interesting that despite this complexity, it often is the case that certain traits in an offspring can end up being what appears to be a simple weighted average of the traits of the parents. When you think about though, the genetic reshuffling that occurs as parents' DNA merge, does not allow anthing like an operation of "taking the average". Fundamentally inheritance is boolean and alleles are either passed on or not.
On the other hand...
Hypothetically, if you did have "numeric" genetic sequences, averaging of the values might take the form of a new kind of dominance relationship between the pair of alleles. If they were neutrally dominant, half the time one value would be used, and the other half the time a different value would be expressed. This could result in a fluctuating production level of a hormone which over a short time would average out to the midpoint of the parents' values. Of course, in another situation this could result in the left arm being several inches longer than the right.
It is fun to kick these ideas around a bit.