A 3,600 year orbit is just as possible as a 76 year orbit, 76,000 year one, or a 365 day one. The path and cycle of an object’s orbit around the sun depends on many variables however the focal points are it’s velocity, trajectory and range from the (sun).
The known planets have a similar elliptic plane, except for Pluto which has a high deviation. Pluto hasn’t even experienced one solar year yet, since it’s discovery. All orbital cycles are different, so Planet X might not traverse anywhere near Planet Y for XXX number of cycles. It all depends on their velocities and trajectories. (plus a slew of other sources for deviations)
Sitchin isn’t disbelieved because of faulty physics, he’s disbelieved because of Nibiru.
My opinion of IndianaJone’s Q; should astronomers discover another planetary body (close to Sitchin’s Nibiru) I doubt he will be credited, because he didn’t find it! Many astronomers do believe there is another body out there, and are actively looking. I think they would get any credit where credit is due…