Rather by chance, I stumbled across the solution:
In the Servers view, and upon right-click of the local development server, there is another context menu entry "Google App Engine WTP / Deploy to Remote Server". This will deploy the EAR and all modules to the Google infrastructure. There is also a "Google App Engine WTP" button in the Servers view's menu, offering the same options.
Frankly, I find this a highly inconsistent UI implementation: If we create a project of type Google Web Application, then the Google button in the main menu is effective, and the context menus can be found as "Google...". These become invalid (but are still present) when we create a multi-module EAR structure in the WTP style. This will create a different set of buttons and context menu entries, all in different places, and the context menu of the LOCAL server would then support deployment to the REMOTE server.
UPDATE: After using the GAE tools for a couple of weeks, I finally switched to the command line options (appcfg) for remote deployments. I had additional errors in GPE for deployment rollbacks (which fail in Eclipse but work with appcfg). I recommend appcfg as administration tool for the Google infrastructure, it provides more control and it is more mature than the Eclipse plugin.