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Get that THM-350 rebuilt to handle the torque/hp the new engine will put out. If you do much highway driving, you would be better to swap-in a rebuilt 700-R4 that can also handle that amount of load.
Once you decide on the tranny, call and talk to the techs at a brand-name torque converter supplier. Tell them what you have and what you want. They will tell you what you need for a converter.
DO NOT let some grunt desk jockey at a parts store talk you into any converter 'he/she would recommend'.
Which ever torque converter company you contact, have your cam specs card right in front of you. They will need to know at what RPM your cams power band is in. The cam and converter have to work together.
the 400 is a little stronger but may sap more power
Id just build up the 350 put a high quality converter as these guys said or put an Od in it. Youll never regret it will totally change the personality of the car youll find yourself doing a lot more driving esp hwy
Dont fall for those cheapie converters youll be sorry.
The turbo-400 is a very 'heavy duty' unit that will hold up to about anything. But, it is also heavy, inefficient, has no overdrive gear, and you would still need a torque converter.
Swap out your present transmission for: 1) another THM-350 that is built to take the power of your new engine; 2) a stoutly built overdrive transmission that will give you better off-the-line starts AND comfort & economy on the highway.
The one thing you do NOT want to do is stay with your present transmission. If you do, you won't have it for very long.