There is currently no easy-to-use way to export a DOM model and deploy it to another agent in an automated way. There is however something on the horizon that will make this very easy in the future.

This, of course, does not help you now. Currently, there are a few ways on how this could be approached, but as suggested by Tom & Jochen, this will involve some custom code in the installation script of a .dmapp package.

You can either create some custom import logic that will read the DOM data from JSON/files & send them to the server using the DOM helper (that is what the extracted DOM editor code does that Jochen suggested), or you could code the entire DOM model deployment in a script. The latter is the most robust but would require you to write code that instantiates & builds all DOM configuration objects (SectionDefinitions, DomDefinition etc.) in C# and sends them to the DOM manager on the server. Depending on the size of the DOM model that was already built (using the DOM editor I assume), it could require quite some extra work.

In terms of the soft-launch question. It is possible to adjust the soft-launch file from a script since it is just an XML file. But like Michiel already warned, take great care when enabling these. Unfortunately, there is no way around the restart.  (may depend on what soft-launch features are enabled, but in general, almost all need the restart.)