mysql replication and GRANT that doesn't quite grant

I am trying to set up mysql replication. All's well, but I see an error 1045 for the slave:

mysql> show slave status\G
*************************** 1. row ***************************
               Slave_IO_State: Connecting to master
                  Master_Host: <my.host.ip>
                  Master_User: slave_user
                  Master_Port: 3306
                Connect_Retry: 60
              Master_Log_File: mysql-bin.000001
          Read_Master_Log_Pos: 107
               Relay_Log_File: mysqld-relay-bin.000003
                Relay_Log_Pos: 4
        Relay_Master_Log_File: mysql-bin.000001
             Slave_IO_Running: Connecting
            Slave_SQL_Running: Yes
              Replicate_Do_DB: my_db_name
          Replicate_Ignore_DB: 
           Replicate_Do_Table: 
       Replicate_Ignore_Table: 
      Replicate_Wild_Do_Table: 
  Replicate_Wild_Ignore_Table: 
                   Last_Errno: 0
                   Last_Error: 
                 Skip_Counter: 0
          Exec_Master_Log_Pos: 107
              Relay_Log_Space: 107
              Until_Condition: None
               Until_Log_File: 
                Until_Log_Pos: 0
           Master_SSL_Allowed: No
           Master_SSL_CA_File: 
           Master_SSL_CA_Path: 
              Master_SSL_Cert: 
            Master_SSL_Cipher: 
               Master_SSL_Key: 
        Seconds_Behind_Master: NULL
Master_SSL_Verify_Server_Cert: No
                Last_IO_Errno: 1045
                Last_IO_Error: error connecting to master 'slave_user@my.host.ip:3306' - retry-time: 60  retries: 86400
               Last_SQL_Errno: 0
               Last_SQL_Error: 
  Replicate_Ignore_Server_Ids: 
             Master_Server_Id: 0
1 row in set (0.00 sec)

mysql> 

I try connecting manually, it starts out fine, but I've a permission problem. I can connect but I can't see anything but the info database:

$ mysql -h my-host-name -u slave_user -p
Enter password: 
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 46
Server version: 5.5.49-0ubuntu0.14.04.1-log (Ubuntu)

Copyright (c) 2000, 2016, Oracle and/or its affiliates. All rights reserved.

Oracle is a registered trademark of Oracle Corporation and/or its
affiliates. Other names may be trademarks of their respective
owners.

Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.

mysql> show databases;
+--------------------+
| Database           |
+--------------------+
| information_schema |
+--------------------+
1 row in set (0.00 sec)

mysql> use my_db_name;
ERROR 1044 (42000): Access denied for user 'slave_user'@'%.my-domain.com' to database 'my_db_name'
mysql>

But on the master, I created the slave user thus, which seems to be more than adequate:

CREATE USER 'slave_user'@'%.my-domain.com'
IDENTIFIED BY 'changeme';

GRANT REPLICATION SLAVE ON *.* TO 'slave_user'@'%.my-domain.com';

(In passing: I think I would have preferred GRANT REPLICATION SLAVE ON my_db_name.* TO 'slave_user'@'%.my-domain.com';, but that is an error, and I should get this working first.)

mysql> select * from mysql.user where user = 'slave_user'\G
*************************** 1. row ***************************
                  Host: %.my-domain.com
                  User: slave_user
              Password: *la-de-da-da-nothing-to-see-here-hashed
           Select_priv: N
           Insert_priv: N
           Update_priv: N
           Delete_priv: N
           Create_priv: N
             Drop_priv: N
           Reload_priv: N
         Shutdown_priv: N
          Process_priv: N
             File_priv: N
            Grant_priv: N
       References_priv: N
            Index_priv: N
            Alter_priv: N
          Show_db_priv: N
            Super_priv: N
 Create_tmp_table_priv: N
      Lock_tables_priv: N
          Execute_priv: N
       Repl_slave_priv: Y
      Repl_client_priv: N
      Create_view_priv: N
        Show_view_priv: N
   Create_routine_priv: N
    Alter_routine_priv: N
      Create_user_priv: N
            Event_priv: N
          Trigger_priv: N
Create_tablespace_priv: N
              ssl_type: 
            ssl_cipher: 
           x509_issuer: 
          x509_subject: 
         max_questions: 0
           max_updates: 0
       max_connections: 0
  max_user_connections: 0
                plugin: 
 authentication_string: NULL
1 row in set (0.00 sec)

mysql> 

I do have reverse DNS configured. I've restarted both mysqld instances in a bit of just-in-case cargo culting.

Any suggestions?