Rearrange docker build script.

Rearrange docker build script.

Disambiguate build layer dependencies, now that Docker build
automatically parallelizes multi-stage builds when possible. This change
clarifies which layers are reused and which are unique. This minimizes
overall CPU time for fresh builds, but more importantly ensures that
components from separates stages are not subject to race conditions in
the resolution of dependencies that are satisfied through package
managers. It should also improve maintainability by reducing duplicated
logic.