If your stock RFT are able to run vibration free, to me the problem has to be in your tire/wheel assemblies.
Yes a Road Force balance is different than a normal spin balance. You can read more about the machine on Hunter's website. In a nutsheel, the machine tries to not only balance the wheel/tire assembly, but also measures lateral and radial forces that can contribute to vibrations and your car wanting to pull in one direction. For example, you could have a tire/wheel that is in perfect balance, but the tire or wheel has excessive run out. This run out would exert a force that could be felt through the automobile's suspension system and up through the steering column or driver's seat. The driver would feel a vibration where the tire balancer would indicate all is well. In this case, the shop might try rotating the tire on the wheel to see if the Road Forces could be reduced. If that doesn't help, it might indicate you have a bad tire.
Bottom line, a Road Force balance is better and can diagnose and correct many issue that a traditional spin balance wouldn't. Hunter Road Force balancers are consider "state of the art" and are a lot more common than they were several years ago. You should be able to find a shop that has one in most mid sized cities are larger.