Many thanks for the suggestions
My new HDD has just arrived, and I already took a comprehensive backup of the two faulty HDDs with Paragon Backup&Recovery.
Tonight, I will take yet another backup with Microsoft's migration tool - now Windows Easy Transfer (which helped me a lot, when I migrated from WinXP to Win7), then tomorrow I'll make the jump.

Thank you all again for your support. I will report back here, when migration is successfull, and let you know how all this went.