How would you build a 416 Stroker 340?
KB makes a forged stroker piston for 408/416 engines in .070 over. the part number at hughes is 2308+070 its a step dish piston they're only 52$ a piece. they also have a listing for a part number 2020+070 for a hyper stroker piston for 408/417 engines they are 40$ a piece. as far as i know the compression height of these pistons are the same whether they are in a 360 or a 340 with a 4" stroke, and should not go any shorter than 1.250" or the wrist pin will interfere with the bottom ring. according to the website the compression height on the 2308 is 1.465" and on the 2020. the step dish design is going to poke out of the deck, which shouldnt be a problem with open chamber heads, but if the blocks been decked and the heads are milled you could be in trouble if you use them. on the 2020s based on a .030 overbore and .039" compressed gasket they list the CR as follows:
58cc = 10.0:1
62cc = 9.65:1
70cc = 8.99:1
74cc = 8.70:1
stock 340 heads are usually about 71 - 72 cc. i've got a few j heads that are milled .010 and average around 69cc's. if you were to use a thinner gasket you may be able to squeeze a little more compression if you needed it.
moper is right though you need a big set of lungs for a stroker. if your 340 heads are the 2.02" type with some porting they may do the trick, but if you are looking for a racier setup or plan on doing more track time that road time i'd step up to something else from the aftermarket to really unlock the strokers potential. i agree with moper on the 750 being used up after 5k, but how often is this care going to see that RPM. you said a streetable engine and with a 750 you should make it ok on the street.
just my 2 cents