Here's a head scratcher that I want to run by everyone...
I replaced the 40 year old OE harmonic balancer on my 1970 340 4-spd with a new internally balanced dampner from Summit. After installation, I now have a a speed dependant vibration with the new dampner. 
The dampner is a Summit street/strip piece that "looks" good. Compared it to the original 1970 piece and they look identical accept for the OE dampner has a sheetmetal part on the back that I'll call an "oil slinger". I ran the engine from idle to about 2500 rpm and had bad vibrations everywhere. The vibration seemed to reduce in intensity the longer I let the engine run. Behind the wheel, the vibration was very evident in the seat of the pants and mirrors. Under hood though, operating the throttle by hand, the engine seems to run smooth with no obvious evidence of vibration.
I did replace the dampner a year ago and had the same issue. At that time I had just re-wired the car and didn't want to deal with another problem so I re-installed the OE dampner and returned the new one. The vibration disappeared once the OE dampner was reinstalled.
Nothing about this makes sense. This is the second time it has happened and I'm curious as to if anyone out there has run into this similar situation.
Thanks in advance for reading this far...
You mention speed dependent so I assume that the problem can be reproduced in any gear within the same general RPM range, right? If that's the case then you're looking at the right area (in front of the trans).
You mention that it gets less the longer the engine runs. Could something be heating up and expanding, possibly, making the vibration less intense? Does it go away completely or just noticeably reduced?
I've been fighting a similar condition with my car ever since I finished a complete restoration on it 2 years ago ('70 Cuda). In my case, however, I have a very noticeable vibration that comes in at around 3700 RPM along with a generally rougher than normal feel when cruising at lower RPM's. When I am under the hood bumping the throttle it seems fine (smooth), but when I'm in the car reving it I feel the roughness, just like you mentioned. When I'm on the road cruising as soon as I hit 3700 RPM I feel my vibration kick in. Now, I may have 2 separate problems with my car. One with the roughness and another with the vibration above 3700. Yours it sounds like just a vibration and at lower RPM's than mine. I have a 4-speed and I noticed that if I run the car up above 3700 RPM and push the clutch in and let it out slowly the vibration goes away and I can cruise above 3700 from that point on. I still don't know why but at least I have identified a characteristic behavior that could lead me to a solution to the vibration part of my problems.
For the general roughness issue, I considered replacing the damper to see if that had an effect and I may still do so. I suppose a slipped, or slipping, damper could cause it to be out of balance if the components that slip are out of balance by themselves. When I look at my damper when the car is running it appears to be concentric and not wobbling. Not sure if that is indicative of anything or not. I do know that proper damping is more important than just correcting an annoying vibration. Its main purpose is to dampen the power pulses transferred to the crank so that you don't break it. So if you have a problem with an imbalanced damper it is important to fix it.
Someone else asked this in this thread and I don't recall seeing a response, but why did you replace the damper if it was not giving you a problem? Have you tried replacing it with the original one to verify that the problem goes away?
I'll be following this thread closely, as it certainly has some similarities to my own problem. Good luck finding a solution.
