Interesting theory but it seems to me that once set in motion it would be hard to get them to settle into regular orbits. Add gravitational effects of the other planets and it seems that it would cause even more erratic orbits.
Cool stuff fer ponderin anyway.
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.