WordPress MySQL writes during "Flush Tables With Read Lock" are rejected instead of being queued
It is a brave soul indeed that still uses an all-MyISAM database.


  Why are writes being quietly discarded instead of being queued, as they would be for a regular table lock?


Look at the error message again


  [20-Nov-2014 01:41:56 UTC] Wordpress database error The MySQL server is running
  with the --read-only option so it cannot execute this statement for query 
  INSERT INTO wp_options... 


WordPress is reporting this as the error, but it not a failure on the part of MySQL. You turned on read_only. That's what WordPress sees.


  And more importantly, how can I fix that so they DO get queued and are eventually run in the order they were requested? :)


Just remove read_only:

FLUSH TABLES WITH READ LOCK;
system time cp -pdRu /mysql_data_dir/thedb /backup_dir/thedb
unlock tables;


The DB Connections should start to queue up all INSERTs, UPDATEs, and DELETEs.

You said something far more profound in the question


  Both reads AND writes need to be possible during the backup. But the backup time is very short, so it's fine for the writes to be queued until the "unlock tables" command.


SUGGESTION #1

You need to convert all your tables to InnoDB. Reads and Writes can continue and queue up just fine without FLUSH TABLES WITH READ LOCK;. You would dump the database like this

MYSQL_USER=root
MYSQL_PASS=rootpassword
MYSQL_CONN="-u${MYSQL_USER} -p${MYSQL_PASS}"
MYSQLDUMP_OPTIONS="--single-transaction --routines --triggers"
mysqldump ${MYSQL_CONN} ${MYSQLDUMP_OPTIONS} thedb &gt; thedb.sql


SUGGESTION #2

If you want everything to remain MyISAM, your should get another DB Server and setup MySQL Replication. All your writes would happen on the Master. On the Slave, you would do the backups like this

STOP SLAVE;
FLUSH TABLES WITH READ LOCK;
system time cp -pdRu /mysql_data_dir/thedb /backup_dir/thedb
START SLAVE;


You can also split your reads between Master and Slave, or do all reads on the Slave.

EPILOGUE

If you go with SUGGESTION #1, convert everything to InnoDB with this script

MYSQL_USER=root
MYSQL_PASS=rootpassword
MYSQL_CONN="-u${MYSQL_USER} -p${MYSQL_PASS}"
MYISAM_TO_INNODB_CONVERSION_SCRIPT=/tmp/ConvertMyISAMToInnoDB.sql
SQL="SELECT CONCAT('ALTER TABLE ',table_schema,'.',table_name,' ENGINE=InnoDB;')"
SQL="${SQL} FROM information_schema.tables WHERE engine='MyISAM' AND"
SQL="${SQL} table_schema NOT IN ('information_schema','mysql','performance_schema')"
SQL="${SQL} ORDER BY (data_length+index_length)"
mysql ${MYSQL_CONN} -ANe"${SQL}" &gt; ${MYISAM_TO_INNODB_CONVERSION_SCRIPT}
mysql ${MYSQL_CONN} &lt; ${MYISAM_TO_INNODB_CONVERSION_SCRIPT}


GIVE IT A TRY !!!

UPDATE 2014-11-21 10:52 EST

In your comment, you just asked


  Is there any major reason to NOT install a 2nd MySQL instance (the slave) on the same server?


There is a huge reason why you do not want to setup a 2nd MySQL instance on the same box to do replication.


Everything is MyISAM
MyISAM only caches indexes, never data
MyISAM defers caching data to the OS
Master and Slave caching the same data in two different DB means twice as much data for the OS to cache
See my other reasons in my old post Is it unwise to run replication on same physical server?


If you convert everything to InnoDB (which caches data and indexes, has failsafes for crash recovery and transactions), then, yes, you could setup a 2nd MySQL instance for replication on the same server (provided you have sufficient RAM and diskspace for the 2nd instance).