I agree with everyone here Devon....I myself, would seriously look into a better block, or well, a BIGGER CID to put a turbo or even blower onto it if its HP you want, its more CID you need. and with larger CID, comes better chances of wehat your trying to achieve with less.
In this case more IS better......You'd almost be better off with a generation 3 Hemi, small, but economical to use in this one as the 5.7 or even the 6.1 would be simpler to do what your trying and FIT in the space of the said 340 you had planned with in the first place. WITH less dollars spent.....
A833 tranny, new or used? Say, $1,000 used, $3,000 new (somewhere there abouts)
Again, the tranny would need built as well, to handle the torque of the super charger/blower turbo (whatever you want to call it) but that stresses the motor a bit, and that all leads into the tranny. Built it last longer, as either or a show car, OR track car.
As for the set up, AGAIN, go with something more beefy then the 340, it will last longer, and NOT kill your wallet. As you watch it........AGE!