Balancing a 360

Hello everyone.

I have taken to restoring a 1973 Scamp that I bought while I was awaiting medical retirement in the Marine Corps. It's been quite a learning experience and curve balls keep being thrown in my direction. I have had the vehicle running and all seems well at the moment, however I've been reading up on the 360 and how it is externally balanced and I seem to have a lot of vibration in my engine. As this is the first engine old school V8 I have built, I'm not sure if this vibration is simply the motor doing its thing, or a symptom if engine imbalance. I used an OEM replacment cast crank from Eagle that is externally balanced, along with the stock rods and aftermarket Speed Pro dish pistons. I used the OEM balancer and flexplate. Is there a certain way for the flexplate and balancer to go on? Also, would it be worth my while to have this engine pulled and taken to a machine shop to have it internally balanced? I'm going to be driving this vehicle back to Chicago from San Diego in the upcoming week or two and want to make sure everything is in tip top shape for the trip. Don't really want to do any side of the road repairs.

Thank you very much for the help in advance.