You could do as you are talking about with taking the transmission to the shop, but if the balancer did slip and that is causing your vibration as redfastback gas suggested just balancing the transmission to the balancer will not prevent the balancer from slipping again.
If you don't want...
I'm still realatively new here so forgive me if this sounds foolish but why didn't you replace the positive battery cable? It sounds to me like the cable that supplies the starter with the current needed to turn the motor over may have internal corrosion or a bad connection?
:newb: