Assuming a 1 BR would be sufficient, four 2BR weeks at Marriott's Grande Vista can be locked off into four each 1 BR & studios and reserved consecutively. One could join II and almost certainly upgrade those studios to a 1 BR if they wanted. Total cost going in at or under $10K ($2000 per 2BR week plus closing) and yearly fees for 2018 under $5500. If ones joins II and upgrades them, that adds another $1000 to the cost yearly between membership, exchange and upgrades fees. Or if a 2 BR is needed, buy 3 BR or combo of 2 & 3 BR villas and use the same principles though obviously more expensive but likely only by about $6K additional going in and another $1400 yearly for all 3 BR options. The points systems aren't going to be very efficient for this situation but would be very flexible. It's likely that just a house or condo rental will be cheaper but might have less amenities and options. I was able to find evidence of 2 fractionals but they don't appear to link to timeshare exchange options and I don't know if any of them will fit your needs though worth finding out.
One thing owning at Marriott's GV (and not all weeks there or any of the other Orlando Marriott's, would be the ability to use Marriott's Florida Club (Grande Vista, Ocean Pointe, Legend's Edge, Beachplace Towers, Doral). Theoretically you could own several of them and use to reserve at GV just as I described above but you'd also have other locations you could reserve.
The advantages of doing the timeshares are flexibility, options, cleaning and amenities. IF you can find a private owner to rent a condo or home from, I suspect you could get a nice place for cheaper than the Marriott maint fees. Wyndham points could put you effectively on property but would be more yearly, but you could reserve directly for the entire time and have direct access to their other options for other locations. Bluegreen would be cheaper to buy in but only 2 BR so maybe $2-4K going in but yearly fees of $8K roughly to reserve directly. One option for the gambler would be to buy less Bluegreen points based at the Fountains and try to get bonus time at 48 days out. If one is OK moving periodically, owning elsewhere and exchanging in for all of the needed time might be cheaper still but more aggravating and the risk of having to move. And even possibly own and exchange through RCI to DVC, esp at SSR.
Lots of options, just exploring them to help you think about the various options, costs and risks involved.