The plot thickens again. Having translated the linked text of Graetz 1889, I see he points out that the discrepancies come from another circulating version (in Provencal) which changes the location from Toledo to Arles.

More important, he finds a key context for these, published in an edition of the 1507 El Libro Verde de Aragon originally written by an Inquisition secretary, Juan de Anchias (whose bio is found in History of the Inquisition by Henry Lea, vol. 2, 1906, and in the Jewish Encyclopedia). This work was thought lost but after discovery was republished by Rodrigo Amador de los Rios (1849-1917) in Revista de Espana, year 18, vol. 106, p. 568 (1885).

The appendix in Amador de los Rios shows that the letters were believed to have played a part in the very historical solicitation of Archbishop Juan Silecio of Toledo to Pope Paul III to impose strictures to exclude Marranos (birth Jews proclaiming Christianity) from church office in the 1540s. They seem tailor-made for such a purpose, on top of their literary idiosyncrasy (e.g. "satrap" was in use in Spain but was incongruously put in the mouth of "Ussuf" in Constantinople where it was not common). While such an appendix would not have been original in de Anchias, it does demonstrate a historical place for them:

"Estas cartas fueron en parte causa que el dicho Arçobispo Siliceo recavase con el Padre Santo, Papa Paulo tercero, que ningun confesso pudiese obtener beneficio alguno en la Iglesia mayor de Toledo, porque el Padre Santo lo rehusaba mucho por lo mucho que podian los judios en dicha Iglesia, que casi toda estava en poder dellos por la mayor parte, como sus Arziprestazgos y Canonicatos y otras dignidades; pero vistas por el padre santo estas cartas y otras infinitas scripturas, que descubrian la malicia é maldad dellos, concedió al dicho Arzobispo que confesso alguno no pudiese tener canonicato ni beneficio alguno, como lo vemos por experiencia, que para hauer de servir por escolano en alguna capilla de la dicha Iglesia, se haze probança de cómo es Christiano viejo, tan auténticamente como se puede hazer para ser official del Santo Officio."

Translation: "These letters were partly the reason why the said Archbishop Siliceo petitioned the Holy Father, Pope Paul III, that no confessor could obtain any benefice in the main Church of Toledo, because the Holy Father strongly [or often had] refused them due to the great power the Jews held in said Church, which was almost entirely under their control, including their Archpriestships, Canonries, and other dignities. However, having seen these letters and countless other writings that revealed their malice and wickedness, the Holy Father granted the said Archbishop permission that no confessor could hold a canonry or any benefice, as we see from experience, that to serve as a choirboy in any chapel of the said Church, proof is given of how one is an Old Christian, as authentically as one can be to become an official of the Holy Office."

Graetz writes (translated):

Both letters, the question as well as the answer, are written skillfully enough to produce the desired effect; they were intended to convince Paul III that the conversion of so many Jews to Christianity was merely a charade to destroy the Church. Paul III effectively protected the Marranos; he had long opposed the establishment of the Inquisition in Portugal, tolerated the Marranos' presence in Ancona, and turned a blind eye to their tendency to practice Judaism .... The supposed correspondence exchanged between the Jews of Spain and those of Turkey was meant to prove to him how dangerous it would be for Christianity to entrust priestly functions to false Christians. It is undoubtedly for this purpose that these letters were fabricated. Moreover, Archbishop Siliceo had to rely on the Pope's credulity to convince him that these letters had been discovered in the archives. For it seems strange that the Marranos deposited them there, at the risk of revealing their evil designs to all of Christendom: usually, more care is taken to hide such compromising documents.

Graetz goes on to charge Silecio with the forgery directly; he had written the Estatuto de Limpieza 1547 calling for pure ("Old Christian") blood for all benefice holders in Toledo. Silecio also made a misleading statement about the 1491 trial over the Holy Child of la Guardia (for whom nine Jews were killed, including Benito Garcia who confessed under duress to a murder of 1487, but for whom no murder and no body was ever shown to have existed). He placed this event as "de poco tiempo aca", of little time past, making it appear a recent risk of Marranos rather than a 60-year-old event, and the controversy over his use of this trial was reported in a manuscript cited by Graetz as Fidel Fita. Silecio may also have retaliated in kind with satire, because Marranos began "to affront him with injurious pasquinades and words, until they forced him to defend his honor and make inquisition" in response (Amador de los Rios: "afrentarle con pasquines y palabras injuriosas, hasta obligarle á satisfacer su honra y hacer inquisicion"). The name "Chamorro" reflects the family of pronotary Felipe Clemente (a prisoner of the Inquisition) who had all changed their name from Chamorro upon conversion. This name change was listed by de Anchias in the genealogy of the Libro Verde, and also noted by Cardinal Mendoza y Boabdil.

Also, in Amador de los Rios, the letter was allegedly not found in the archives by "Benito Selyagio", the hermit of Salamanco who appears to be a character created by Medrano, but by Silecio.

Graetz concludes by demonstrating that the Arles correspondence in Provencal is clearly the copy of the Toledo original, even though it adds a date of "13 de Sabbath 1489" (probably meaning 13 Shvat 1489, which the Protocols abusively translate as 13 Jan 1489, but which would be proleptic Gregorian 24 Jan and Julian 15 Jan). He gives several notes that the 16th-century circumstances of Toledo disagree markedly with 1489 Provence. He thereby proceeds to charge the editor of the only publication of the Provencal letter, J. Bouis, Avignon 1641, with making the fitting changes to the Spanish letter to continue the pattern of persuading the pope against tolerance (now in Avignon), of alluding to the blood libel (a case in Venice 1477 that contributors here have probably missed, and Simon of Trent 1475), and of getting facts wrong (putting the name "Simon" in Venice and saying such child was canonized as a holy martyr).

Now, one problem with Graetz is that a detective might argue the case is too neat: two different men with the same charged motives engaging in the same fraud and errors a hundred years apart. But it's demonstrated that both writers did use the "blood libel" and that at least one version is a forgery variation of the other; and the earlier appears forged due to the incongruities that are obvious prima facie even in the OP presentation. So despite the poetic parallelism it appears that we can confidently say there was never a member of the Clemente (Chamorro) family who received such a letter from someone known only as Ussuf (Joseph) about the "satraps" of Constantinople and then allowed such a damning letter to be preserved in the archives of Toledo just when Silecio needed it to make a case he had been making for years. The use of forged letters by other Catholics for dispute settlement has been observed before. As I previously noted, the poetic justification of the alleged Jewish revenge as mere tit for tat was not inflammatory for its actual ruling: it was clearly because Catholics felt that converted Jews had not truly adopted Catholicism and thus their strictures against the Jews were called into question if they were, even hypothetically, to be met with vengeance on the same scale. The guilty Catholic conscience created most of the crisis. If Silecio was the forger, he was projecting upon the Jews his own doubt about the use of power upon them and his own rationale based on what he believed they had planned to do against him. Proactive tit for tat is the worst form of open war.