I got my hands on a 2000 Buick LeSabre with the 3800 V-6 that seems to be OK for the most part except this annoying problem.

Starts and runs fine when cold. Will run all day long if started cold. Shut it off and let it sit for 30 seconds after it's warmed up and the problems start. It will stumble, usually die, but not always. Sometimes it stumbles a few times and then clears up. If you give it gas while it's stumbling, then it dies out. It will restart but it is difficult to do so. Then, after restarting, coming to a stop will usually cause a stall.

It's throwing an evap system code but I doubt it's related. I know the ignition module is usually suspect here but it seems more like it's starving for fuel, though I could be wrong.

Anything common with these that I should look for?