I did a lot of research on Tundras because I'm thinking of selling my T100 and going to a Tundra. What I found is that the 2000-2002 Tundras have a lot of overdrive transmissin problems. They start exactly the way you describe with it slamming into OD from third. Apparently there is something wrong with the planetary gears/bearings. If they pull the pan there will likely be a bunch of metal in it and they will tell you that you need a rebuild. I'm sorry I couldn't have a better story for you but thought it would be good to let you know so that you don't spend more money on flushes, etc.

I had my trans go on the T100 due to a hose breaking going to the cooler. It ran dry and fried it. The rebuilt cost about $2600. The shop told me about the Tundra problem as well. Do a search on the internet and you will get a lot of info. So much info that I decided to hang on to my T100.