I still stand by my post too much stroke and hp for a thin wall casting like the 340. and if you are going to use sticky tires especially at the drag strip with a prepped track (VHT or equivalent traction compound) you better get a bigger rear axle. the 8 3/4 will not take the abuse. a dana 60 will but the car wont handle as well on the street. too much unsprung weight. a good choice would be the poor mans dana which is a dana 44 out of a 90's grand Cherokee. its all aluminum, way stronger than a 8 3/4, will take drag strip abuse and is easily modified.
if you do go with the 408 and continue using it as a daily driver, pm me in a few and tell me how may miles you got out of it before you windowed the block. most savvy racers running a small block hard block the water jackets, use studs instead of head and main cap bolts and run a girdle. or they do the really smart thing to do, they get a race block and use studs instead of bolts with a girdle.
that 340 was a fun little motor in its day and you can make big power with it, it just wont live long with the abuse. remember motors are built up to drive hard.