The Sun and Jupiter so outweigh all the others (in terms of momentum if nothing else), the worst that can happen to them is to be alternately thrown out of the Jupiter/Sun system, or the Sun/Jupiter system while at the same time, easily kept captive by either one or both in quite circular orbits.
In the outer part of the ring you have a Uranus/Neptune/Saturn/Jupiter system. Here the intermediary planets retained their gas shells (I believe only one of 'em has a rocky core though ~ that'd be Jupiter). They have dramatically different mass though, and Neptune regularly gets tossed out of its orbit, whipped around, jerked this way and that, and ends up cockeyed.
I guess that makes sense. Even a wildly erratic orbit would still regulate over time unless a planet were thrown entirely out of the solar system. (which leads to a whole new set of interesting ideas)
I know that many of the extrasolar planets we’ve found have far closer orbits to their suns or orbits more akin to comets.