While your idea sounds good on paper, it doesn't really hold much water
when inspected carefully.
Any time you hang a specific start and finish date on a cruiser, trouble looms. First, the time interval (13 specific days) is rather short. Even if your putative cruiser is actually ready to leave on the promised day (and that is not all that likely), weather
can prevent a safe departure for days. In the early cyclone season there are often lows developing in the ITCZ near the Solomons or northern Vanuatu
. The majority of them fizzle out, but every few years one develops into a named storm, so one has to watch them carefully, for their track crosses your proposed route.
At any rate, the distance from Fiji to Vila is on the order of 700 nmi, and to Noumea around 800. For most cruising yachts this means 5 to 8 days of sailing in moderate conditions. Could be faster, could be lots slower if the winds aren't there or something breaks. Thus, any delay of the start would mean that you would miss your (supposed) flight out. I personally, as one pretty experienced in that part of the world, would not undertake to deliver you on that sort of schedule.
On the other hand, there will still be lots of folks headed in your direction at that time. We don't usually make the trip back to Oz from the islands until late November or even early December. We do watch the wx carefully, and have cyclone anchorages
sussed out ahead of time.
So, while I don't think it is realistic, I wish you luck in your quest.