Hi, Philipp-
That kind of result for affine allignment isn't so surprising--happy to talk more about nonlinear alignment if you have questions.
Integrating nonlinear alignment with @SSwarper and full FMRI processing with afni_proc.py is probably the most recommended way to go. If you want your final subject data in subject anatomical space for some reason (which is perfectly reasonable!), you can still use afni_proc.py and @SSwarper, just not using the results of the latter in the former directly.
Just let us know what location for "final" data makes most sense, and we can discuss options for processing.
-pt