There isn’t a quick How To for what you are after as I indicated on the other thread. Omnibus takes care of packaging, config management like Chef takes care of configuration. These are entirely separate things.
Omnibus has it’s own DSL that can be used to do “configuration like” things but again it’s specifically geared toward producing packages of the DEB/RPM/MSI variety. That is to say, you can probably do much of what the cookbook you have does inside an Omnibus definition but there is no integration so to speak, these tools have very different design goals. For example, chef-client is an omnibus package but we still have a chef-client cookbook to manage the config files and such. How much you want to blur the separation of concerns is up to you here but there isn’t really much written along doing what you’re after specifically.