Mariadb – Manually modify master-bin.index

I have an issue with MariaDB Server 5.5.56 replication. The slave got stuck and when I realized that we had already lost some of the bins. So this is the scenario :

In master :

MariaDB [(none)]> show binary logs;
+——————-+————+
| Log_name | File_size |
+——————-+————+
| master-bin.000320 | 1073742333 |
| master-bin.000321 | 1074247558 |
| master-bin.000322 | 753717941 |
| master-bin.000323 | 883803465 |
+——————-+————+
4 rows in set (0.01 sec)

cat master-bin.index
./master-bin.000320
./master-bin.000321
./master-bin.000322
./master-bin.000323

In slave ( excerpt )

MariaDB [(none)]> SHOW SLAVE STATUS\G
*************************** 1. row ***************************
Slave_IO_State:
Master_Log_File: master-bin.000312
Read_Master_Log_Pos: 405852801
Relay_Log_File: mariadb-relay-bin.000942
Relay_Log_Pos: 405852988
Relay_Master_Log_File: master-bin.000312
Slave_IO_Running: No
Slave_SQL_Running: Yes
Exec_Master_Log_Pos: 405852703
Relay_Log_Space: 405853426
Seconds_Behind_Master: NULL
Master_SSL_Verify_Server_Cert: No
Last_IO_Errno: 1236
Last_IO_Error: Got fatal error 1236 from master when reading data from binary log: 'Could not find first log file name in binary log index file'
Last_SQL_Errno: 0
Last_SQL_Error:
Replicate_Ignore_Server_Ids:
Master_Server_Id: 1
1 row in set (0.00 sec)

So my idea to try and recover the slave is :

1.- In master : stop mariadb service
2.- In master : copy from backup bins 312 to 319
3.- In master : manually add bins 312 to 319 to master-bin.index
4.- In master : start mariadb service
5.- In slave : start slave

Would that work ? Is there any other way to solve my problem ? I know manually modifying master-bin.index is not recommended but I can not think of any other alternative to avoid recreating the slave.

Thanks in advance.