It's complicated, but the date of the FIRST composition was almost certainly July, 1785 (a choral version using a male chorus and a "cantus firmus" vocal line), followed by a purely instrumental version in November for the memorial service for the 2 prominent Masons (The Masonic Funeral Music). The July entry had to have been written in November since the event (the deaths/funeral music) was listed along with it. But in Mozart's catalog, he listed the MFM ahead of K.478 which was written in October. That sequence is one of several clues that he wrote it in a month preceeding October. For the category of the month of November, he did not enter the MFM. Why not? Because he wrote the piece in July - at least the CHORAL version. The 2 versions are nearly identical with the choral version essentially being the MFM with a chorus (for the most part). 
I have a copy of Mozart's Thematic Catalog. 
Mozart mistakenly (?) entered K.478 under July also (rather than October), but at least he entered the sequence of the 2 pieces correctly: K.477, K.478. There's other evidence, but it gets very lengthy and complicated. The sequence of those 2 pieces in his catalog plus no mention of the MFM in November should be sufficient evidence that the original music for the MFM was not composed in November. It was just a VERSION of it which was done in November, nearly identical to the first one. He dated the MUSIC correctly, but omitted the first and lesser event of the elevation of a visitng Mason to Master in August. Doing catch-up work on his catalog in November, he listed the more important event: the deaths of the 2 Masonic Brothers in November for which it was performed again. 

2 events, 1 set of music (essentially), composed prior to K.478, correctly listed under July for a Masonic ceremony in August, but the more important event (the deaths of the 2 Masonic Brothers) accompanied the entry, written in November due to some administrative procrastination on Mozart's part. 

Mozart normally entered the MUSIC only once in his catalog, not repeating an entry if it was essentially the same music for a different Event or purpose. 
In other words, his Thematic Catalog was primarily a book of Music - not Events, even though he also listed the event or person or opera, etc, along with it.
For example, if one of his operas was revived or produced in some city for the first time, he didn't list it again in his catalog. That would be an Event-Driven catalog. 
And in doing catch-up work on his catalog, evidently sometime in November (after November 7th when the 2nd Mason died), he listed the music as having been composed in July, but listed the event as being the deaths of the 2 men.
1 set of music, 2 events, the more important event listed in his catalog.    
His catalog is slightly messed up on that page, but mostly correct, and with pieces listed in the correct sequence - which may have been more important to Mozart than listing the correct date. 

If someone says "July must be a mistake", they need to have their ducks lined up and explain why he listed the MFM prior to an October piece, and why he didn't list it under November. 
The "mistake" theory is a push-button ejection seat, in some cases, and carried to extremes, one could claim that Beethoven wrote the MFM, with scholars mistakenly believing that it was Mozart's handwriting on the score and in the catalog. 
If "July" was a mistake, prove it. 
I think July is correct, and there's a great deal of evidence to back it up - the first piece of evidence being that Mozart said so in his catalog. 
Web page article coming shortly.

Dave Morton.