360 engine vibration

George Jets, your pretty much on the money with your comments. The block casting number reads 360LA dated 1978. The rockers look used and have that used dirt to them, they are on a shaft so assume this confirms they are LA heads. Heads look recon with new clean valve springs. The engine oil has been changed and remains clean, this lead me to think its recently rebuilt.
The new speedo that was fitted showed 7 miles and there is zero wear on brake pads and shoes. The block has new core plugs and all gaskets look recent, suspect the unpainted water pump is a new one. I suspect its a fresh rebuilt motor with little miles as its the same throughout the build.
Someone spent some serious money on this. Its has a fresh rebuilt 727 trans, ford 9" back axle, all new brakes and suspension front and rear.
The converter is new with no weights and i have fitted a B&M externally balanced flex plate (see photo below).
The ignition is stock expect me upgrading to GM HEI. Is there a difference between magnum and LA front dampers? Could it have a magnum crank in an LA block? The crank has a notch out at the rear where the flex plate bolts on does this suggest LA crank? ( see photo below)
My thoughts at present are a balancing issue or cam timing out of whack. Or cam not broke in correct and worn lobes. I need to check all valves are fully opening with rocker covers off.

But this is my first V8 and mopar, so steep learning curve. I'm more familiar with straight sixes or flat fours, so all help appreciated.
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