My 95 LeSabre had a similar problem. The way my mechanic explained it to me was that there was a fuel line coming out of the gas tank that had a clamp come loose. He tightened it back up and the smell went away.
You can remove the access plate in the trunk and look at the fuel pump assembly (and hoses) where it goes into the tank. Fill your tank, and have a look for leaks. You might also look at the filler tube going into the tank for leaks, but you will need to get under the car to see this.
I had a strong gas smell from a 97 Lesabre. It was leaking gas from the where the fuel line meets the metal fuel line that goes into the tank. I ended up putting in a section of high pressure fuel line from the tank to the fuel filter with 2 clamps on each end.
I don't recall the gas smell going away when the tank reached less than 3/4 though. I would look around the fill tube (as mentioned) and the vent tube for the tank to see if it is leaking out there, like where the rubber tubes meet the tank. The clamps may be loose or there might be some other leak going on problem.