When the manufacturer "stretches" a Lincoln Towncar to build a limo, they lengthen the passenger compartment. The trunk is not touched by this process. Fortunately, the Lincoln Towncar has a huge trunk to begin with.
I've never hired a stretch limo in Orlando (only sedans and vans), but I've often used stretch limos in the Chicago area once even with seven people going to O'Hare Airport. When there's too much luggage for the trunk, the driver puts some bags on the front passenger seat and floor. And we've taken our carry-ons into the passenger compartment.
The short answer is that the limo's trunk is likely to be insufficient for six people, but, if you don't take too many large bags, there are other places to accommodate the remaining luggage when the limo's trunk is full.
In comparison, a regular Lincoln Towncar sedan can get really tight with four people and luggage because one of the passengers is sitting in the front passenger seat so no luggage can go there.