I had the exact same problem with my 383 blower setup, early 2 piece block, using the Eagle 4340 crank and 5.7 rods with a set of JE pistons I bought off eBay. My machinist said he could grind the crank throws a little, the small amount needed for clearance, the only issue would be balancing costs. These pistons were originally custom forged for an LT-1 motor, why they didn't fit I don't really know. I spoke to Eagle's tech and they said they have seen interference problems but never with JE pistons until now, and also recommended grinding the throws. I spoke to JE and without the original order number they couldn't help at all.
I didn't want to cut a new relatively expensive crank, so I sold the pistons and bought a set of JE "shelf" blower pistons with the -31 cc dish and they cleared fine. I didn't want to go with the 6" rods because of the pin interference with the oil ring location.
I didn't lose any $$ so I was lucky in that respect. What part number are your pistons? If you decide to go my route I'll get the part # for the pistons I'm using.
Also, those pistons won't work on a 6" rod anyway, they have a different compression height.