Hi mate,
Installing the crank and pistons out of a 3T into a 2T block is a common conversion done by the 2TG twincam fanatics to obtain 1800cc's of engine displacement up from the original 1600cc's.
I believe the 13T is the 1800cc 3TC in some sort of pollution guise. The parts therefore are interchangeable so far as pistons and crankshaft as a set can be installed from one engine to the other as the only difference between the 2T and 3T is the longer stroke of the 3Tand shorter piston gudgeon pin height, hence why crank and pistons change over as a set. The rods are same length so either set will fit.
Small caution here is that I have also read that the 13T engine may have a different combustion chamber shape to the 2T's hemispherical chamber so the pistons will need to be checked carefully for fitment. You may need to grind the 2T block a small amount to clear the longer 13T crank also.
Cheers,
Jason
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