Is This Common For a Custom-Built Torque Converter???

The fact that it has been balanced, presumably neutral balanced is a good thing. Any quality converter that I have had has had some balance weights, albeit most neutral ones have only had small weights to make them neutral. I too have found that the aftermarket flexplates from B&M have the holes about 1/8 to 1/4" too close together, compared to a stock flexplate, and they must be slightly opened up or elongated to work. I wouldn't rule out that the problem is with your flex plate.

That being said, that does look like a lot of weight to obtain a neutral balance and makes one wonder about the quality of workmanship that went into the building of that converter.