Do I have to re-balance this 360

The 584 grams is WITHOUT the pin. And the pin is considerably heavier than the KB pin. So you are making a biiiig change in the reciprocating weight..... it's absolutely time to re-balance.

To minimize delays, if you are so inclined and have the tools and capabilities, you can balance the rods yourself but this is some work. You have to balance the total rod weight, and also balance each small end against each other, and each big end against each other. That takes the right setup to weigh big and small ends. Or, since you are in a hurry, drop the $300 or so on a set of SCAT rods I-beam rods which are already balanced 100% as a set and they give you the balance data. The KB piston set should be super close between pistons and pins. (But double check anyway.) With that, all that needs to be done with the rod, piston, pin, ring, and pin lock weights, is to compute the bob-weights, which is just a straight calculation, and give that and just the crank to the shop.

2+ years? That was a serious problem; if it had not been done in a few weeks tops, I would have been back pulling the parts out of that shop. Just manage the situation right and you won't have that issue again. Go to another shop obviously!