If your saves were not in the cloud, then were saved only locally on your PC.

If the huge problem you mentioned spared the information on your hard drive, you could try to copy those saves into the newly installed game. But I think this is an obvious thing and you already considered this possibility.

If I would loose my progress, I would either
- use cheat commands to give myself the resources I had and I would build a new base in a new world or
- I would start from scratch and try enjoying the game again.