How about an object rotated on the normal/anti-normal axis? I understand an object on the same orbital plane having a problem staying stable, but if the orbit is swung into the Z-axis, you introduce different orbital characteristics for apoapsis and periapsis such that flinging the object out of Sol’s SOE is more complicated.
Well, say changing the orbital plane were enough to make the orbit stable. That would mean the planet’s orbit wouldn’t cause massive disruption to the inner solar system during that portion of its orbit.
It’s really an either/or proposition. Either it can have a stable orbit, or it can cause massive disruptions as it travels through the inner solar system. Both can’t be true at the same time, because we are dealing with a finely tuned system built on feedback from all the moving parts.