The approach you have detailed looks like it will do the trick. I would make only a few changes to it due to my own personal worries and desire to always have a back out path:
1) Rename the offending folder on your HDD rather than delete it,
2) Remove the offending folder from Lightroom (remove only; no delete from disk at this point),
3) Import photos (copy Copy as DNG) from saved card(s) making sure "don't import suspected dups is checked. This is a good time to decide whether to let Lightroom perform a rename for you and/or select a folder to copy the imported photos to; and
4) Verify that the catalog looks correct and photos are now stored as you want them; and finally
5) Delete the offending/renamed folder if everything looks good.
You can also make a full backup (separately/locally) to use as a recovery point. Again, this is just to have a point in time you can return to. It may not be correct but at least you would be no worse off if something goes wrong. Again, my own paranoia having lost many nights of sleep fixing problems caused by 'simple' system changes...
