And meanwhile I just deployed the package to our production server. Here it did run just fine. So apparently we only have this problem on our test server. Will check...

So I just returned to my testing desktop, where I left the package running. However, after 8 minutes the first task and the package failed after all.

Error: The SSIS...

No, none.

I do need to rectify something: there actually are locks while running the package, but they're all S or IS locks.

No, there are no locks while the package is in running mode. When I change the package tranOption to NotSupported both tasks run as expected, but obviously there would be...

MSDTC service is running. I don't get any error. The first task just stay's yellow (running) and won't continue after validation.