I just found the Solution by accident. I removed the explicit setting of the voncersion exit:

cl_salv_column_table( r_salv-salv->get_columns( )->get_column( <dropdown_columns>-columnname ) )->set_edit_mask( <dropdown_columns>-conv_exit )

and instead, added it to the Domain itself. Then i changed the dropdown values from domvalue_l to ddtext to show the text. Now the automatic check accepts it and the texts are show as wanted, but still uses the ID internally: