Thanks for your reply, but I'm afraid it isn't of any help so far.
I have set the variable as you requsted:
@ini_set('display_errors', 'on');
I started the migration run again.
Like yesterday, everything works just fine up to step 5 (see the attached screenshot).
It is at 27.56% and seems to have frozen there with no change for almost 2 hours now.
And sadly no error messages either. Or do I need to check a log file somewhere?
Cheers,
Matt