How would you build a 416 Stroker 340?

I can tell you that $3K is cutting real close to the low limit. You can run your heads, as long as they are done well now. The intake will be uslesss over 4K rpm..there's just not enough port or plenum there. There are "take offs" on the RPM Air Gaps, but I'd look for a swap meet M1 single plane if the real deal Air Gap is too much $$. The carb is way too small. A 750 on a 4" stroke engine is all used up by a little over 5K, so you'd be looking for at least a 780ish Holley Avenger or something like a 800DP 4150 series (as a budget saver...). Manifolds will not move enough air, but cheap headers can do what you want without loosing much. About the only other thing you can re-use is the block, and I'd run factory rods done with ARP bolts long before the cheaper new rods, but that's me. You might be able to get it done for that beign careful. But the pistons will be the biggest cost. More than the crank, because nobody makes a .040 over piston as an "off the shelf" deal. You can get them easy, but they cost more. I dont think KB makes a 4" stroker piston for 340s..They do for 360s IIRC. I wouldnt use a cast or hyper piston with a 4" arm tho. At 6K you are at about the rpm limit of hypereutectic piston (in terms of piston speed). A cheaper alternative might be to get your hands on a 360, and re-build that. You'll need the 360 only flywheel, but the rest can be used, even the manifolds, and it will make great usable torque..(tire smoke comes from torque, not HP...lol) You'll get more from a well done performance 360, then a ultra low budget 408 IMO.