It's so automatic that I had to think hard as to whether I'm mis-reading something in your post, but this is what we do to deploy reports.

We set up project configurations and deploy by right clicking either the individual report or the whole project in visual studio (BIDS)

In solution explorer window:

right click the solution (tip, set tools, options, projects and solutions to have Always show solution ticked) - it's the top item of the lot

Choose configuration manager and set up the three different configs. dev Test and Live in our case.

Then right click the project (below solution) and choose properties and set up your target report server details, datasource folder, overwrite datasources etc for that configuration. Save and repeat for each configuration.

By selecting the correct configuration property for the solution, you can then right click one or more reports (multi-select) to deploy to the correct server with a click.

If I'm copying a load of reports from one server to another I use the rsscripter tool