I've been doing some research into the development of the idea of teaching the classical languages using modern intuitive methods. 

An early 'modern method' teacher, called Jean Manesca, appears to have written the first fully developed modern language course in the early 1820's - designed for French, he was keen to see it adopted for the classics, and actively promoted the idea. His "Oral system of teaching Living Languages Illustrated by a Practical Course of Lessons in the French through the medium of English" was entered at the library of Congress in 1834.
In his introduction, on pg xix, Manesca writes

" If I have not spoken of the advantages that may be derived from the present mode of teaching applied to dead languages, it is not because I entertain the smallest doubt of its efficacy in that particular; for, on the contrary, I am confident that many years of toilsome, tedious, and almost fruitless labours, would be saved by the adoption of such a method for these languages. A well disposed young man, between eighteen and twenty, well versed in the principles of his mother tongue, would, in twelve months, acquire a sufficient knowledge of Latin or Greek for all the purposes of life. Such a consideration well deserves the attention of the few scholars competent for a task which would prove so beneficial to the present and future generation of collegiate students. The present modes of teaching the dead languages are sadly defective. It is high time that a rational, uniform method should be adopted"

Shortly afterwards, Henri Ollendorff adopted Manesca's methodology, and produced the famous series of books using the 'Ollendorff' method, which follow Manesca extremely closely. I had revived Manesca's course, which I was using together with Ollendorff's French textbook, as it was  well suited to podcasting. 
Mypodcast went bankrupt in January 2012, and closed its servers. 

I have since then re-issued some lessons from Manesca at my YouTube channel.

As I sit here, I hold in my hands a copy of the "Nouvelle methode pour apprendre, a lire, a ecrire et a parler une langue en six mois, appliquee au Latin" - by H G Ollendorff, written in the 1840's. Adler's American edition, which I am using was an extensive revision of Ollendorff's first Attempt - Adler includes the grammar - Ollendorff's French text is extremely light on the grammar, and is almost entirely intuitive, learning is based on practice alone, not theory. The book has 600 pages of very fine print, with copious, and I mean copious exercises. Adler also expanded the Latin text, resulting a much higher quality textbook, with much more elegant Latin, and a wider variety of examples based on the historical classic sources.

Adler's text,being an Ollendorff, is inferior to the method originally devised by Manesca. Ollendorff picked up the outline of the method from a student of Manesca's, called Mr Albert Brisbane,who visited France from the USA,and engaged Mr Ollendorff to teach him, using the method he had outlined in manuscript from his previous lessons with Mr Manesca. Ollendorff never fully grasped the structure of Manesca's system, and to my mind Ollendorffian textbooks are defective.

Adler is a direct translation into Latin of an Ollendorff text. Adler did not make up any of the material,  or the sequence of material, he simply translated the text into Latin, and added a parallel Latin syntax.

The French-Latin Ollendorff was, as far as I can ascertain, the first textbook written in modern times aimed at teaching Latin as a spoken language, using 'modern' methods - I don't think Manesca's method was ever translated directly into Latin or Greek, although it did appear in a Spanish edition written by Carlos Rabadan.

 Albert Brisbane's Biography, where he describes in some detail his private classes with Manesca, says that he studied Latin using the same method,but it is unclear who taught him. Perhaps Ollendorff did? If Manesca ever wrote up any Latin exercises, I would be very keen to obtain them - perhaps they only survive in manuscript among his papers. The Ollendorff version went through several editions, and was quite popular for private pupils, but it was never taken up by schools for teaching Latin. 

Adler's American edition seems to have suffered the same fate, and copies of it are very hard to come by. Only ten or so printed copies of his textbook still exist in national library collections worldwide.

So, when people discuss teaching Latin as a spoken language, using modern teaching methods that involve speaking Latin in the classroom, it should be realized that this methodology has a long pedigree, it isn't the new fangled and dangerous thing that some Latin teachers seem to think it is.