Hey Prozac, I also have a '97 ES300 and have had the exact same problem as you're describing. I don't know for sure that my problem has gone away, but I haven't had the problem again. After revving the motor for quite a while, I was able to get it to continue running. Someone here at work thought I might have water in the gas, so I left the car running, purchased a bottle of gas treatment and topped off the gas - at my usual station (last gas fill-up before was a new station I stopped at????????). Anyway, it's been ok ever since, but I do still use the gas treatment from time to time.
Maybe you can give this a try.
Good Luck!!!!