Engine shakes BADLY!!

Well, that just leaves the leakdown test,and the converter/flexplate...................I think.
Tight or leaking intakes will really suck the idle vacuum down,and then the engine hates a load.
Is it still the same converter on there? And is it a neutral balance?

Well, there is one more thing, I guess; The converter stator clutch, or the tranny forward clutch.
Since you say putting it into gear drags the engine down, I suppose it could be a stator. If the stator was bad, off-the-line torque could be sluggish. A stall test would probably rule it out .
If the forward clutch was out of balance (hard to imagine), that could do it.I can't think of a test to prove the forward clutch.