Calling a flexplate that has the notch out of it 'balanced' is likely confusing to new folks. By itself, it is unbalanced..... so you might have been confusing the OP. Just make it easy to understand.
I've just brought the 318 flex plate to the machine shop and told them to balance it for the 360. They welded a weight inbetween one of the arches. Both times I've done it this way it has worked great. I have one of them on one of my Dusters now.
P.S. - Calling parts incorrectly will certainly confuse new folks. Send them looking for something that doesn't exist. (lol)
To the OP, correct term is balanced flex plate to use a slant six, 318, or 340 torque converter behind your 360. You can buy one from B&M, or you can have the one behind your 273 balanced for a 360.
And to be sure there is no confusion, the 360 is externally balanced, meaning you balance the converter or flex plate to balance the motor (externally is outside the motor). So, when you balance the flex plate, your actually balancing the motor by weighting the flex plate (or converter).