Why not build a 360 with a stroker kit to make it a 408?
340s were good for their time, and still are to a point. They had a lot of hot roddy stuff but were essentially a large bore 318. Car companies always do **** on the cheap if they can get away with it.
In the case of the 273, 318, 340 i believe they all share the same crank stroke and same length rods, and only the bore is different.
360 shares the same length rods, has the bigger bore like the 340 but a longer stroke.
The 340s claim to fame was it could wind up quickly to 6,000 rpm. This made em a 1/4 mile contender. If your planning on a 6 speed manual, modern upgrades and not really going for an original resto because of the vin which will always say its a slant 6, then id recommend to, buy a 360, add an eagle or scat stroker kit and be done with it. Scads of HP compared to the 340, same amount of money spent.
I payed $200 for a mid 70s 360 truck engine and i sold off what i didnt need. Stroker kits w forged cranks for SBM are coming down a bit in price. You can find em for around $1,500 now.
Magnum 360s are plentiful in junkyards now. Stroker kits are the same as for LA 360s. And they are a roller cam engine. Engine quest sells an iron monster magnum head. All new casting eliminates the cracks associated with the stock heads. You can buy em machined for an LA intake bolt pattern, or for a magnum head bolt pattern. I believe they are machined for 2.02 - 1.60 valves. Part numbers are CH318A, and CH318B part number determines how its machined for an intake manifold. Also 5 bolt valve covers will work on the 10 bolt magnum heads.
As far as a manual goes, i cant help you there. I set mine up for an A-833 OD box. I will likely swap that out later on for a passon 5 speed.