logsaver.js provides the ability to save console.log messages to localStorage.
startSavingLog();
You can change the localStorage key used.
startSavingLog({keyForLocalStorage:"SOME_NEW_KEY"});
You can also modify the date formatter. Simply specify a new one.
startSavingLog({timestampFormatter:Date.toUTCString});
stopSavingLog();
clearSavedLog();
removeSavedLog();