I am in the midst of building a 340 stroker. With the big bore of the 340, it will displace 416 cubic inches.
I didn't want to dramatically increase the cubic inches without addressing the heads. Since an engine is essentially an air pump, you need a lot more flow with a lot more cubic inches. I have elected to go with aluminum heads that flow much better than the 340 ported heads I have. In your case, assuming you have standard 318 heads, they would be very restrictive. I would highly recommend a good set of aluminum aftermarket heads. If not, then you should at least open up the intake and exhaust valves on your heads to the 340 valve sizes (2.02 and 1.60, if memory serves). You should port the heck out of them too. Getting airflow into and out of the now 390 engine will be critical to make power.
I am trying to do my 340 stroker build on a bit of a budget. My engine will be for street use on an air conditioned car, so I am building it for low end torque and reliable power with good low end vacuum. I purchased a Scat stroker kit with .030 pistons. It has a cast crank and hypereutectic pistons. It is still good for way more horsepower, torque and RPM than my street engine will see. My engine target is upper 400s for horsepower.
Overall I am happy with the kit so far. They seem to be nice components. My only gripe so far is the rods were slightly over spec so I will need to tighten them up.
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I have not yet purchased my heads nor made a cam selection. This is still up for discussion with my father-in-law. However, we have decided that the cost of roller rockers is not worth it - I will go with a flat tappet cam (again, I am doing this as a budget build). The flat tappet will work fine, just need to be sure we break it in carefully.
Finally, I think stroking these small blocks is really cool. My engine will go back into my 1973 Road Runner. With aluminum heads and intake, it will make for a lighter, more nimble car that will still have lots of power!
Good Luck!
Hawk