I think I would go the acid route, since it seems like it would be simpler for you. Also, if there is Rh, you would likely lose it somehow if you melt to form shot or to cast cell bars. By dissolving, you would get the small amount of Rh in the filter. What you would then do with the Rh is another problem.
Try the process on 1 (or, 3 or 4) ring first. I'm very big on looking before you leap.
If it is sterling (and it probably is), it should dissolve in nitric very quickly without shotting. You might consider 4metals procedure for producing pure silver. It sounded pretty slick and simple to me. He claims 999.9 on the process. Even if you only got 999 or 999.5, it would still be a lot purer than cementing on copper. You could form AgCl and reduce it, but that procedure is often fraught with problems. Here's the thread. Read all of 4metals posts on it.
http://goldrefiningforum.com/phpBB3/viewtopic.php?t=1275&postdays=0&postorder=asc&start=15
To dissolve four pounds of sterling, it will theoretically take about 2.6 liters of concentrated nitric plus an equal amount of distilled water. In practice, it usually takes a bit more. Were it me, after proving that it is silver and that there is no problem dissolving it, I would:
(1) Put the 4# in a 5 gallon plastic bucket.
(2) Pre-measure the nitric and the water.
(3) Cover the silver with some of the water, about 1/2" above the silver.
(4) Under a hood, add some of the nitric - maybe about 1/4 to 1/2 liter. It should quickly start fizzing. Allow it to work until the reaction slows down. Give it a gentile stir, occasionally. Add more nitric and repeat. If it goes too fast, add more water. The object is to add the nitric as fast as possible with no foamovers. When all the nitric and water are in (maybe 30 or 40 minutes later), stir it well, cover it, and let it work overnight, preferably not in a cold area. Make sure all of the water was added or the solution may crystallize when it cools.
(5) By morning, all of the nitric should be used up and all, or most, of the silver dissolved. Let it settle and decant or siphon off the solution. If there is only a little silver remaining, dissolve it in a minimum amount of 50/50 nitric. If there's a lot of silver remaining (there shouldn't be), there will also be a lot of free nitric remaining. You may have to put the same acid back on the silver and heat it. I have run 100s of lots of sterling and contact points using the above procedure and it was always ready, except for a little undissolved silver, in the morning.
(6) Filter and recover the silver with one of the above methods.
If you have problems dissolving, try preheating the water. You should have no problems, though, starting at room temp. The reaction will generate heat.
Something I just thought of. The manufacturer may have put lacquer on the rings to prevent tarnishing. If so, you will find this out when you try to dissolve a few samples. You may have to incinerate first.
