I know this is a very old thread but it still shows up when searching and alot of folks still read them so...
So I also had issue on my 2001 T4R 3.4L with starting and then stalling after a 10-20 minute warm soak or after a fill-up. After much troubleshooting and must testing, I found that the installer of a new EVAP canister had reversed the CCV air line and PURGE line connections back at the EVAP canister. What led my to suspect this was the obvious P0440, 441, 446 errors and the fact when warm or after fill-up there was fuel vapro and fumes in the intake hose from the airbox area. Disconnecting and removing the MAF had a very distinct fuel odor. I then pulled the CCV input line from the airbox and was about knocked out by the fuel vapor smell. I knew that wasn't right. The ECU would interpret that as fuel and start warm or after fill-up and stall or severely stumble until it would pick and run, but upon second start would run fine after. so I chased both the PURGE line and the CCV air lines back to the canister and found them reversed.
Try lookin gin these areas for bad, crossed, reversed lines, defective canister or VSVs. your answer lies in those areas.