I have been thinking about same issue lately. As far as I know, the ring represents the section of very slow growth. In my region, Finland, North Europe, growth rings appear during the winter when water temperatures are very low (less than 4 degrees celcius) and the growth speed is minimal. Are your mussels collected from a waterbody where the temperature or some other reason causes the mussel growth to cease annually?
Maybe keep trying with the thin-sectioning techniques. In our experience, it can take some time to find the right angle and thickness to cut for different species & scenarios. Still though, we have also run across populations that are simply really squirrely in their growth ring patterns. This seems to be more common in streams and lakes where mussels are in soft sediments like muck and shifting sands. Still no solution for these situations aside from sectioning enough individuals until you find a few good ones with interpretation rings. There is also something called "mutvei's solution" which might help, but I haven't had luck with it yet. Let us know how it goes and if we can help further...
I know you may be already ready to read the data from the shells and have no time to go back to the filed. However, can you try to stain live animals, return them into the water for a specific time, say one-two years, collect then and see if that provide some way out? You can then try to model what previous ring deposition was and try to back-calculate the ages? I know this is very crude, but can help.