Hughes 27-30 and B&M 10239 will not line up.

No just use that stock flexplate!
It's actually a good thing the B&M won't fit with the weights installed, it's not supposed to as it is the counterbalance. If it did fit, this motor would have got assembled and the weight would have been canceled out by the recessed area and the thing would have shook as if you put the stock 318 converter and flexplate behind the 360.

Actually if you look at the writing on the converter it says 27-30 but under it says 360bal. I assume that's the code they use to mean it's balanced for the 360. That's the converter you need, you just don't need the $90 B&M in addition. I'm going to reuse my stock converter, so I do need a flexplate like that.