Car Stalls after filling with Fuel

I have a 2004 Dodge Grand Caravan with approximately 96,000 miles. Since about September 2008, my car has had a problem with stalling ONLY after I fill up the tank with gas. I fill up the tank, drive away from the station. As soon as I come to a stop, the car stalls. It will start up fine again, and then seems to drive fine after this. I fill the tank about twice a week and at first I noticed the problem maybe every other fill up. For the last 3 weeks, its been consistently stalling every fill up so it seems to be getting worse. I never let my tank get below 1/4 full. I'm not sure how many gallons my tank holds but when I fill up I put in about 13 gallons. I've taken it to my mechanic (who I think is awesome at his job) but basically he says he can't tell for sure what the problem is unless he sees it. He guessing it could be the fuel pump but its expensive to replace this on only a guess. He also says for all the many years he's been a mechanic he's never heard of a car stalling only after you fill up the tank. Any thoughts would be appreciated. If I have to replace the fuel pump I would rather do it sooner than later as I'm always nervous that my car might not start up again after one of these episodes. But, like many people, my home budget is so tight that I concerned about spending $800+ dollars if it doesn't fix the problem.

Thanks!