Your Clematis in the ground will be just fine. It will start to grow back in no time.
Personally, I've never had much luck with rooting Clematis cuttings. They take months to root both in rooting medium with root hormone applied and water. Then, rooted cuttings are very vulnerable when planted in the ground. I would not bother with Nelly Moser which is cheap and widely available. You can still try it, but expect to wait for 3-6 months to see first roots. Soft new growth is likely to rot.

Ditto, toss the cut off stems and don't worry about the plant.

For what it's worth.... I've used green floral tape to 'splint' stems back together. It almost always works, but you have to do it right away. Like grafting, you have to make sure the cambium (green layer just under bark) touches, one to the other. Don't fret. Just put the stems end to end and wrap about 6" of tape around it. Presto!

Mickie

I would just take the broken branches as mother natures way of pruning the stems. Since Nelly is a type II, the damaged stem area may serve as an entry point for wilt to gain a foothold. Whether splinting the branches back together would actually work or not would depend on how damaged the stem was. If the vascular system was disrupted, then putting them back together would be like trying to splint an arm back on a person when the blood vessels had been severed.