What rationale do KJV-1611-Only give for not recognizing the apocryphal books of that version? For the first 274 years of the KJV (including most notably the 1611 version) the KJV included the apocryphal books. So if the 1611 version is inspired why don't the Protestant KJV-1611-Only crowd consider them canonical?
Interesting question (which gets an up-vote from me), and although I am not a “King James Version Only” Protestant, I was curious enough to go looking for a possible answer.  Here is part of what I found...

King James (VI of Scotland and I of England) authorised his translation in 1604 and it was completed in 1611, 85 years after the first translation of the New Testament into English appeared (Tyndale, 1526). In the preface to the 1611 edition, the translators of the Authorized Version, or King James Version, state that is was not their purpose “to make a new translation . . . but to make a good one better.”

While many people claim that the 1611 KJV is the only “true” translation, rarely are they actually in possession of the 1611 Authorized Version of the KJV.  Rather, they have the more readable 1769 Oxford version.  This version does not contain the Apocrypha.  

The KJV Only movement claims its loyalty to be to the Textus Receptus, a Greek New Testament manuscript compilation completed in the 1500s. To varying degrees, KJV Only advocates argue that God guided Erasmus (the compiler of the Textus Receptus) to come up with a Greek text that is perfectly identical to what was originally written by the biblical authors.  However, it seems that the Apocrypha included in the 1611 version came from a different source:


  “Although the New Testament was translated from the Textus Receptus (Received Text), the Apocrypha was translated from the Greek Septuagint (LXX), except for 2 Esdras, which was translated from the Latin Vulgate.  In 1769, the Oxford edition, which excluded the Apocrypha, became the standard text and is the text which is reproduced almost unchanged in most current printings.”  Source: https://www.gotquestions.org/King-James-Version-KJV.html  


It is worth noting that not all of the books of the Apocrypha are included in Catholic Bibles and that it was not until the Council of Trent in the mid-1500’s that they were officially added.  Here is a brief extract from an article on this subject: 


  ”The books of the Apocrypha include 1 Esdras, 2 Esdras, Tobit, Judith, Wisdom of Solomon, Ecclesiasticus, Baruch, the Letter of Jeremiah, Prayer of Manasseh, 1 Maccabees, and 2 Maccabees, as well as additions to the books of Esther and Daniel. Not all of these books are included in Catholic Bibles.  The Roman Catholic Church officially added the Apocrypha / Deuterocanonicals to their Bible at the Council of Trent in the mid 1500’s A.D., primarily in response to the Protestant Reformation.”  Source: https://www.gotquestions.org/apocrypha-deuterocanonical.html  


Two possible reasons, then, why the KJV Only movement may reject the Apocrypha even though it was included in the original 1611 version: 

First, they may not be attributed to Erasmus and the Textus Receptus.    Second, it wasn’t until the mid-1500’s that the Roman Catholic Church officially added the Apocrypha to the canon.

However, since I am not a KJV Only advocate, I can’t speak for them.  All I can do is present some background information that may have a bearing on your question.