I wouldn't think that a heavy, on-time, period while on an estrogen based birth control means miscarriage, but I guess it could. Depending on how "large" the clots your talking about are, they're probably normal... and clotting isn't related to miscarriage... just to bleeding.
Hormonal birth control can (as you know) dramatically change your natural cycle and flow. You've already experienced it making you have little to no period... now you're having a heavier period. I'd say it's all within the realm of possibility.
If you're worried about it you could give your doctor a call. But unless you're soaking through more than "a pad and hour" it isn't generally considered "too much" bleeding.
Even if you ARE having a miscarriage (which I lean toward doubting since Nuvaring works by preventing ovulation just like the pill) you don't need to go to the doctor unless there are worrying symptoms (like the more than a pad an hour thing).
Again though, if you're worried call the doctor. At the very least it will ease your mind.
HTH
T.