A thousand stardates seem to be more or less a year, so it might have taken six years to ferment. Or then sixteen. Or twenty-six. Or one hundred and fifty-six. Note the absence of the "decade digit" in this 1000 SD = 1 y assumption, meaning that a 8300 stardate can very well be about fifteen years after "Space Seed"...
Were there a Romulan label on the bottle, Kirk couldn't read it, not even the date on it. The TOS heroes don't read alien languages all that fluently - Scotty and Chekov couldn't read Klingon in the following movie. No doubt the label is there for (illegal) export purposes.