Oracle: dbms_repair outputs zero errors about known corrupted object
What's left to attempt?

You can just instruct the database to skip corrupt blocks on a table scan:

begin
dbms_repair.skip_corrupt_blocks(
  'USER',
  'TABLE_NAME',
  dbms_repair.table_object,
  dbms_repair.SKIP_FLAG);
end;
/


Then scan and move the whole table (except corrupt parts):

alter table user.table_name move;


Finally disable skipping corrupt blocks:

begin
dbms_repair.skip_corrupt_blocks(
  'USER',
  'TABLE_NAME',
  dbms_repair.table_object,
  dbms_repair.NOSKIP_FLAG);
end;
/


Alternatively, you can set event 10231 and run the export:

alter system set events '10231 trace name context forever, level 10';


Then run your export. Finally, you can disable the event for future sessions by:

alter system set events '10231 trace name context forever, off'

and 

dbms_system.set_ev for existing sessions. Or just simply restart the instance.