New crate 408 engine is around $7k, 340 around 12k, I have no idea, why that difference. More I think about it and read the comments and experiences, I want to buy just the block and have it built locally.

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I would absolutely put another 340 in it, either 416 version or stock stroke.
Regards price, I have never understood why people say how much more a 340 is than a 360.
Just goes back to Mopar guys being ultra cheap skates in a ton of cases.
You can find a good 360 block for 100-200. You can find a good 340 block for 500-700.
Other than that trivial difference( in the whole scheme of building a motor and putting it in a 30-40 thousand dollar car like the OP)...The difference amounts to next to nothing
If someone is going to whine about 4 or 5 hundred bucks difference in buying a block and then building a motor with it being a make or break thing, they probably have zero business starting such an undertaking in the first place.
If it came with a 340, try and put one back in it.