I have a 1996 Crown Vic Police Interceptor. I have a strong oder of gasoline in the car and no visible gas leaks. The smell is when parked or driving and it seems to be strongest when gauge reads between 3/4 full to 1/4 full.I have replaced the tank due to a leak and thought it would solve oder problem but the oder is still persistant inside car. I know of another car same model and year that has same problem.

Check fuel pump hanger assembly seal
Check filler neck seal
Check spring-lock couplings on hanger assembly for leaks
Check fuel filter area for leaks
Check fuel tank breather

I had a gas smell once that was strong inside the car, I did not spot any leaks then I traced the fuel line along the frame until it was out of sight where it went above the frame right behind the RF tire,
So I pulled the plastic inner fender off and found the fuel line coming out over the frame and swinging over to the engine compartment. And There was a pin hole in the line in this section and was spraying on the plastic inner fender.

A leak here where its below the cabin air intake area would certainly bring gas fumes inside the car

Those police interceptors had a history of smelling like gas. Most commonly the problem was caused by the improper mounting of police equipment in the trunks.These holes were on the top side of the tanks. Is it possible that you new tank was installed and has been punctured by the same mounting hardware of the old tank. The symptoms would be exactly what you have described,the fuller the tank the stronger the oder, and generally do not see a leak because the hole is located on the top of the tank and is small enuff just let the oder out.