I solved the problem by creating a new table as suggested by hotwebmatter. It was quite easy because i could use the structure of other field collection fields and just rename the value field. The structure looked like this:
field_collection_item__field_sprechzeiten_zeitraum: table
+ columns
bundle: varchar(128)
deleted: tinyint(4) NN
entity_id: int(10) NN
revision_id: int(10)
langcode: varchar(32) NN
delta: int(10) NN
field_sprechzeiten_zeitraum_value: varchar(255)
+ indices
bundle: index (bundle) type btree
revision_id: index (revision_id) type btree
+ keys
#1: PK (entity_id, deleted, langcode, delta)
After creating this I purged the field collection entities (there was a link in the uninstall section) and removed the remaining fields in my content types.
The checkbox to uninstall the module was still disabled, so I deleted every table in the database containing field_deleted_data and field_deleted_revision. This didn't help, so I searched in the config table for the line with the name core.extension. Here I deserialized the data, removed the part with field collection, and serialized it again.
In between I always run the cron job and purged the caches.
The checkbox to uninstall was still disabled, and by chance I saw that field collection checkbox in the module install section was not checked anymore. I checked it and tried to install it. It started and I was then forwarded to the module install section. the field collection was still unchecked and when I examined the uninstall tab it was finally gone.
This was gruelling, but with a happy end.