What torque convertor do I use?

BluePrint Engines 408's are all "LA360" balanced on the REAR.
do not confuse that with the fact that we use the Magnum balance damper on the front.

As @Professor Fate mentioned, 340's are unique in balance.

it'll depend on if your previous 340 was stock balance, or had been rebuilt to be internal balance.

chrysler also balanced the converter, and used neutral flexplates, where most aftermarket companies build neutral converters, and use the flexplate to balance.

I would also doubt that your current converter would have the correct characteristics (Stall speed and such) for the bigger, torquier, cammed, 408. unless that 340 was a really stout piece.

you'll most likely want to call a good converter company like gearstar/yank (330) 434-5216, and have them build you one specific to the car. or...ship them that one and have them re-stall it, and balance it properly.

remember, converter is typically balanced as neutral when going aftermarket. in which case you'll just need an an aftermakret flexplate for a 904, with LA360 balance.

gearstar will set you straight on all that, and want to know your weight, rear gears, cam specs, etc.

thats my recommendation. hope it helps.
Ok thanks guys I talked to the salesman and he said it was an externally balanced rotating assembly? The 340 is a 69 block according to the casting.stock other than a slight cam. I bought the car a few years back dont know too much about the engine other than that