HELP!! Huge vibration

My 65 Fastback is giving me a fit.  I am having huge vibration and almost inability to start when on a steep grade.  When on level ground it is almost not noticeable with a very slow clutch engagement.  It seems to run out fine once moving.  

I have replaced the clutch and pressure plate (Centerforce Dual Friction)and replaced the motor mounts.  The transmission is a 1984 T-5.  It has a 9" Ford rearend with nearly new mid-eye leaf springs and nearly new balanced drive shaft. The engine is a full roller 289 with approximately 375 hp but the vibration occurs no matter how softly you try to engage the clutch when on a steep grade.  

I am at my wits end, not to mention the costs.  Can anyone help?  

Bad U-joint on tranny yoke?
Does the clutch chatter and grab upon release on a hill or does the drivetrain just vibrate?
Please explain in more detail.
What is your rear end ratio?
What kind of cam do you run and what is the manifold vacuum at idle and idle speed?  

65fstbkrestomod, I don't mean to sound elementary but, my response is for everyone. Could it be that the angle (to level) of the trans and the third member on the rear is off a few degrees. When the rear was installed if it wasn't checked and set correctly then this could be the cause of the vibration. Use a magnetic angle that you can pick up at most auto or hardware stores and check it. Choose a good flat machined surface on both to measure. They should be the same angle.  

It sounds as if your talking about clutch chatter that has been talked about several times in here. Do a search for "clutch chatter" in the forum and you will see some ideas.  

If you have a stock 2.80 rear axle gear and a big cam in your motor that only allows 10.5 inches of manifold vacuum at idle you could be loading the motor down trying to start on an incline. Less cam and more gear might help if all the other things seem OK.
Early Mustangs are famous for clutch chatter, especially with some aftermarket equipment. One Ford insider said the only clutch that wouldn't chatter much in an early Mustang was the original FOMOCO clutch/flywheel that came with the car or the genuine Ford replacement parts. He might be biased but having run a top loader 4 speed in a '65 for years with various cluthes I would have to agree with him.