Thanks for the hint! I certainly deem myself adventurous enough to try your solution
The only reason why I am not trying it is that I only need to migrate about 10 domains and I am not willing to do the extra work; croydons solution works well enough for me. It is no problem to migrate the databases manually.
But still: we have 3 different approaches to migrate client data between two servers. I am sure that if we picked the best parts out of each, we could assemble a better solution.