I got it working. I saw this, https://apple.stackexchange.com/questions/127665/you-do-not-have-the-necessary-read-write-and-append-privileges-on-the-selected and after plugging the disk into my...

@Kevin_Z That is correct. Interestingly, I first selected the G: drive because I hadn't set up the H: drive yet in the preferences. I was able to add that to the Time Machine preferences without...

@Riley_S Thanks, but my router setup is more like Case 2. There is no Sharing account setup on the router site, only the Read/Write and Read Only access authentication and I have that setup done.

After setting up a sharing account on the "USB Storage Device" page and enabling Time Machine on the "Time Machine" page and selecting the H: drive which shows the correct capacity, when I try to add...