I don't think you are going to get a waggy rear axle into the J10, much too narrow and the perches are not even close for a swap over.
Should be a tag attached to the diff cover giving you the gear ratios.
Since you have not seen it (don't have it apart) it may not be the ring and pinion, could be a busted shaft, could be a number of things.
I wouldn't get to worked up over it until you know what's really going on, swapping ring and pinion will mean resetting the gears.
2000 Infinity QX4, 3.3L, MPFI, 4 speed auto, 2 speed Nissan tcase, Unibody, IFS front, 4 link rear solid axle with 255-70/16s
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