Del the OP said 3 wires from main to the Barn, 2 hots and Neutral. Why I asked if the OP could get a Ground from the Main to the Barn!
I do not like seeing seperate ground rods at the out building's due to potentional "Differences" but Like
@dadsbee says it is his best choice at this point.
If it was me, and getting a ground from my main to the Barn was going to cost Thousands of Dollars regretfully. I would Drive a Ground rod at the Barn, ensure the neutral was unbonded, add a ground block in that SP.
Run a 4 wire of the approprate size to the new shop following the same principle of floating Neutral. Add a supressor at each the Barn and the new Shop! JMO!