Finally the decision has been made.

So I have a question about the torque converter for the 360.
I know 360s are external balanced so the converter is balanced with the engine.
1st) is the harmonic dampener part of that balance?
I need a new one the original one looks shot to me.
2nd) when I replace the converter how is the best way to balance it to the engine?

Yes, the harmonic balancer is part of external balance. B&M does sell a balanced flex plate so you don't have to worry about having a weight welded on the TQ converter.

*Edit* The balancer's are keyed, they can only be installed on the crankshaft one way. *Note* Do not lose the key! Easy to do and PITA to find if you dropped it and it bounced it's way to some obscure dark corner of a inter-dimensional portal that somehow formed in your garage.