I had a 84 Crown Vic Police Package with a 351 windsor and 3.55 rear end with external transmissions cooler, heavy-duty alternator beefed up suspension and brakes, but that is far from today's cruiser. First that car had a body on frame construction, a 2003 will be a unit-body construction. While the engine and transmissions would be fine, you don't have a towing platform to support a large trailer.
That alone is probably why there is such a low limit on the tow rating, not the engine (which in the 2003 is the 4.6L modular I believe, same as the base engine from the f-150/Expedition). Without a ladder frame to connect the hitch-bar to, you won't have the structural strength necessary to support large loads.