Ok.... What RPM does the shake start to become noticeable?
First thought is that if it shakes in neutral when you apply the gas, there is no miss, and the engine isn't bucking because of timing, you might have a broken engine mount, bad tune on the engine to make it run rough, or your thrust bearings just took a dump on you.
I had this issue last year and it all boiled down to my thrust bearings in the engine failing. The engine was smooth until gas was applied and RPMs came up. It would do it in neutral and while driving. After running through all the possibilities, I took the tranny off the bell housing and started the engine to make sure it wasn't something in the tranny. It wasn't. Removed the starter, bell housing, and then put my hand on the clutch and noticed the clutched moved in towards the front of the engine by 1/4 - 1/2" and could move the whole clutch/fly wheel in and out of the engine while connected to the crank and of course, the balancer would move with them. This = new engine.
So it begins. You will get a lot of answers from this forum on what it could be, but you need to take this info and check each one..... Who knows, it could be something that none of us have experienced. Please keep us tuned in to what you figure out!