Clue on timing of Felix felicis potion

[Auria]

No: HPFGUIDX 139959

Something unexplained in HBP I think may be significant - see what 
you think.
In the chapter 'Sectum sempra', Harry reads in his potions book that 
Felix felicis takes 6 months to make.  However Horace Slughorn was 
persuaded to join Hogwarts during July, just before Harry's birthday 
celeb at The Burrow, and Slughorn first presented the Felix felicis 
potion to Harry's class near to the start of term (probably around 
Sept/Oct I would guess) - it was definetely before Slughorn's 
Christmas party anyway.   So that means the Felix felicis potion 
could not have been made by Slughorn within this time, as it is less 
than a 6 month period.

This leads to a couple of possible conclusions:
1.  Maybe the Felix felicis was already being brewed by someone else 
at Hogwarts for another purpose.  Perhaps (and this is pure guess on 
my part) it was Dumbledore, who may have been using it during his 
hunt for the horcruxes?

2. The potion could have been prepared by Snape.  Again guess work, 
but he could have started brewing for either his own use or again 
someone else's, exactly who and why depending if you believe the ESE 
or ESG theories on Snape.

Whatever the reason, I feel this inconsistency in timing for brewing 
the potion could be a deliberate clue by JK Rowling.  Something 
seemingly insignificant, and just 'dropped' into the text, but turns 
out to mean a lot.

anyone have any comments? 
Auria