Sounds to me like you are using a shotgun to swat a mosquito.
These lowlifes are already looking at jail or prison (if convicted), the cost of defending themselves, etc.
Now, you expect to take them to court for the value of the only item not returned (the ring), with absolutely no chance (or expectation) of recovering anything.
Sorry, but your attempts to 'coerce' them into turning over the ring in response to your lawsuit will probably be an exercise in futility... and an additional cost and burden for you. What makes you think that a civil judgment, even one for thousands of dollars, will mean anything to them. They will probably let you have your default judgment, especially considering that they are already proven criminals. These are not 'normal' citizens. They do not care about credit reports, bank garnishments, etc. or any other process that you would need to enforce your default judgment. And maybe, in a few years, they might be back out and working, and you might be able to garnish wages, but that still won't get your ring back.
I would suggest, if not done already, that you talk with the DA and let them know the importance of the ring to you. See if one of the crooks will plea for a few years off on return of the ring.
Other than that, you will just keep 'opening the wound' if you don't let it heal.