You're wrong. Pistons and crank are different; possibly the rods, but not likely.
With a smaller stroke, the 1jz block is actually a 2jz block cut down about 0.5 inches off the deck. Pistons are oil cooled, but they're different than the 2jz pistons. In fact, the asymetrical cutout in the 2jz piston skirt is to account for the longer stroke and clearance for the oil squirter. Interestingly, the 1jz pistons does not have the cutout due to the smaller stroke. Valve cutouts and piston dish are different, too.
The exhaust ports also have a different bolt pattern than either of the 2jz motors. Therefore, using any 2jz exhaust manifold is out of the question. Even if the exhaust were the same, you could not use a 2jz downpipe, assuming it's bolted into the tranny bracket, because the block is shorter. The dp would actually extend 0.5 inches below the bracket.
There are probably other performance part differences between the 1jz and 2jz motors, but I don't sweat the small stuff.
-scott
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'95 sc300 6-speed, AEM, 1000cc inj, TT LSD, RLTC, DIS4, FMIC
sp63 turbo, sp mani/dp/wg pipes, blah, blah, blah