All of the planets have elliptical orbits, thanks to Johann Kepler, but Neptune's is very close to being circular, and it's one of the gas giants, so I don't understand the point about the gas giants having elongated orbits.
It would take a lot to change the orbit of any of the gas giants. That material doesn't appear to be present now. Jupiter could force the asteroids into the present Belt, but the rest of the planets and asteroids wouldn't do much at all to Jupiter.