Chosen Solution
I am thinking of doing two separate swaps - replacing the battery first and fixing issues with the time via terminal (so my new hard drive will be recognized). Then go back and swap the hard drive. Does this sound like a good idea?
First off, don’t clone MacOS - it hasn’t worked reliably since Lion introduced recovery partitions on some of the newer Macs! You want to backup the Mac and restore it from a backup after clean installing the OS. Second, make sure you swap the HD cable - the original cables are often SATA II and they will not work right with SSDs due to that. Not all of them are bad, but enough are you are better off doing the swap to be safe. It’s one of those issues I fix in these right away as soon as I have it open, so I know it’s been addressed due to how bad a sudden failure can be. Before you install the new cable, the trick is to put electrical tape where the old cable lived before installing it. In terms of where to cover, refer to this photo of my old 2011 13” - I did the same in my 2012 13” when I swapped cables.
