Engine shakes BADLY!!
Okay...let me get this straight, new engine, still shaking?
Then I'm gonna venture to guess that it is NOT your engine that is the problem. I had a 408 do the exact same thing, especially in reverse. It ended up being a slightly warp flex plate...btw, it was a brand new, neutral balanced B&M plate..............................
this will sound crazy, but unhook the trans, slide it back, support the rear of the engine and fire the engine up, see if it still shakes, if not, you know its in the trans/flexplate/converter.