Here's a workable plan for you.
When we took our Lifestyle Visit (LSV) in 2011 we stayed at the Lake Shore Cottages, so I know you'll like it. They are just east of Lake Sumter Landing Square (LDL), the center most location in The Villages (TV). There are only 53 homes in Lake Shore, they have their own neighborhood pool. The location is only about 500' walking from the square and just a 2 minute car ride to Morse Blvd, one of the major north south roads.
With a LSV you are limited to 4 to 14 days and in the winter months it's $150 per day. They will put you in the southern most area right next to Brownwood Square, not central to TV. Since you're looking for 2-1/2 months, the LSV doesn't really suit your needs.
Here is a cottage for rent, (actually if it were for sale, it would be worth $699,000), it's available during your time period. It states owner's use Oct 1 - 16, then rest of Oct available for $1200, Nov. $3180, Dec. $3475 with a $800 security Deposit. Here's a photo of the home. Those rates are a great deal, usually you'll pay $3600 just for a courtyard villa in prime season.
Here's a link with all the info so you can set up your rental.
************.com
Lake Sumter Landing Map PDF, you can print this map or stop by the sales office, which is only a couple of hundred feet from the rental, and pick up a Villages Magazine, they have maps of the squares in every issue.
http://www.thevillages.com/lifestyle...T%20SQUARE.pdf