Copy failing drive in order to retrieve files?

Copy failing drive in order to retrieve files?

I have an NTFS hard drive with a dynamic partition, which I believe is on
the verge of failure (multiple spin-up retries, drive disappears from "My
Computer" in Windows). I have ordered a 1TB drive to replace it, but don't
dare connect the failing drive in case it goes kaput. All the really
important data is backed up, obviously, however it would be convenient if
I could retrieve the medium-importance data on it (which is not backed
up), and copy it to the new drive once it arrives.
I was first considering using rsync to do this, but then I realised that
the NTFS drive is not mountable in Linux due to it being dynamic.
So what are my options? Is it possible to run
dd if=/dev/sda of=/mnt/newdrive/disk.img
Then somehow (how?) mount disk.img and copy the files back?
Or is there a better method? Note that I do not want to make a simple
clone from one drive to the other (for multiple reasons, one being that
the new drive is twice the size of the old).
Thanks very much,
Fela