Mick You didn't say what bell housing is in the car?? Also was it trued to the back of the motor before installing. If it's a Lakewood, Start there and center bell housing, replace pilot bushing. and retry for road test. If this fails the next thing is to locate vibration source. This would mean removing the clutch assembly from the fly wheel and run the motor at the rpm you have the problem with. You will need a block of wood to support the back of the motor. If the vibration is gone, bad clutch assembly or wrong balance on pressure plate or cracked disc. It may be as easy as installing a new clutch. Again make sure that the bell is centered on flywheel, new bushing and reinstall.
What dampener is on the motor?? I had some issues with an ATI one. Until the fluid warmed up I got a bad vibration for the balancer. There is a company that will come for about 1K and custom balance the balancer to the rotating assembly. I think this ius more for Nascar motors.
I am going with a bad clutch if the motor was smooth to start. The other possibility you don't want to know. Are you sure the motor has not downed a cylinder??? Bad MSD ignition cap or rotor???
Oil pressure is good when hot??
Pull the chutch and retest would be first step. Rick L. Mick you can also take the flywheel and clutch asembly to a place that will balance cranks and have this checked. I have done flywheels on tire balancer and found only 1 flywheel out of balance by .75 of an oz. Any one have a good tire machine??