Dear Creighton,
I've never used FTK Imager before.
If I encounter bad sectors, I usually continue and finish the dd-extraction and then try a 2nd run.
Exactly like you did, with different cables/controller/etc - to make sure it's the disk's fault.
If the bad sectors are identical:
I just keep the list of badblocks for documentation and continue whatever forensics work I was planning.
If the bad sectors are changing (like in your case):
First of all, I'd try the whole process on a completely different computer. Just to make sure it's not the reading PC that's at fault.
Every PC I'm using for this, I run
memtest86 at least once before. To make sure that data pipeline is working correctly.
If the badblocks keep "moving", I'd suggest taking at least 3 images.
Now, depending on if you want to do attempt recovery, you either choose the image with the least bad blocks.
And of course keep the badblocks-list as documentation with the chosen image.
OR:
Using a binary-diff tool (e.g.
vbindiff. Works with large files) in combination with the badblocks-list for each image and then try to do cherry-pick the block from an image where its not marked as badblock.
Never done this before on a disk (just files) though...
Just my 2 cents :)