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Is it possible? I am getting trigger happy on a new build and don't want to wait or deal with the hassle of a tall deck.
Not really, this combination would "hit" everything inside the case and require, among other things: (1) special rods that are "smallish" on the big end to clear the cam lobes and cylinders, (2)tons of mallory metal to balance (3) pistons with short comp height
Once you change the crank to even a 4", then you must change everything else. The pistons and connecting rods are specific to the stroke.
Buy a shortblock from a known buuilder instead of trying to reinvent the wheel.
Unless the world has changed over night the LS7 comes with a 4" crank and a 4.125" bore. I have seen people go with the 4.250" in LS1 stuff with no problems other than the short compression height. If you did a 4.125" stroke, you would be looking at a 441 ci or so. Honestly the 4.125" crank used to be popular in LS1's. I ran 9's with an iron block 427 but I always felt that the stroke was just too much.
Just curious why you would say too much stroke? Piston velocity or rotating assembly geometry causing cylinder wall wear? I figured I would try to get as much displacement as possible with the block as hand.