I was already thinking about a batch job, that uploads the packages to multiple servers using DTUTIL.exe
But at the moment I have no clue how to.
Out of interest, how many servers?
Regarding DtUtil, what is your issue exactly? Syntax? Cross-domain issues? How to run it? Something else?
If you haven't even tried to resolve your issue, please don't expect the hard-working volunteers here to waste their time providing links to answers which you could easily have found yourself.