Just my two cents worth. I owned a (then new) 1994 Ford Thunderbird, and my father had bought the same car in a different color a few months before me. They both had the 4.6L Modular SOHC V8 as used on the Town Car. They both used about 4.8 quarts on a full oil change with filter. In fact, I can't recall seeing or hearing of that engine not using the "oddball" quantity when using the stock capacity oil filter. Police Interceptors have oil coolers, and the DOHC or higher displacement engines are different enough that I wouldn't count them.
So, when doing your own oil change, start with 4 quarts. After idling the engine for a minute or two to make sure the new oil is in the system with no air in the oil passages or oil filter, shut off the engine, check the oil, and fill the last little bit to the full-cold line. Just one of those "mysteries of life" things, I guess.
If you are into playing around and putting a larger oil filter that will still fit on your engine, then go for it. More oil capacity generally means more time before the oil breaks down to the point where it will no longer protect the engine, all other things being equal. Likewise if you have an overpowering urge to retrofit a PI oil cooler to your Town Car, go for it. If your car was delivered in a desert state with the "desert package" on it, you will probably already have an oil cooler and wonder why the rest of us can't get five whole quarts of oil into the engine. But if you want to stick to what Lincoln put in the car, then 4.8 quarts of oil is plenty.