A couple of things to note: I restored from TIBU and now my battery is back to normal. Doing that put my apps back to the internal memory card from the extsdcard. At least it seems that way to me. Second thing: I did another nandroid backup and can now see it if I choose to restore it. The naming convention makes absolutely no sense to me but at least now it's there. Still don't know why the 1st nandroid backup isn't showing up from within Safestrap.
Well, that's good news. I hadn't realized you moved apps to the SD card, but I wouldn't think that would affect Recovery operation. However, some apps don't work right when you move them to an SD Card, which could possibly increase battery usage. Some apps will even mention not moving them in the description of the app on the Store.
If you could please do a few more things I would be grateful, as I'd like to know the answers to a couple questions, for helping others in a similar situation in the future.
1- look and see if there is more than one subfolder with an 8 character name (phone serial number) now residing under TWRP/BACKUPS, or if it is still just one folder.
2 - Is your initial nandroid backup also in the same numbered folder as your newest backup? If it is not, move it there and then please see if Recovery can now see it when setting up to Restore a nandroid. If for some reason you move the inital nandroid as I asked, and TWRP still doesn't see it, then it may be corrupt or something.
The nandroid name - Well, the first part of it is a numerical date and time code along the lines of what I like to use. So my code for today, July 31, 2014, at 11:04 AM would be
2014_0731_1104 but they also add the seconds to the end, so perhaps 110452. However, there is a flaw in the process both TWRP and Clockworkmod recoveries use to gather this date and time from the device, and for the past several years both of the teams making those utilities have said they are unable to remedy it. So the date and time are there, but they point to like 1970.
The remainder of the cryptic name can be seen if you open Settings and scroll all the way down to About Phone. Then scroll down to Build Number. I see on my S5:
KOT49H.G900VVRU1ANCG
Which is probably what you see too. It is an identifier for the ROM, if I am not mistaken. Which means if someday our bootloader gets unlocked and you flash a completely different custom ROM, or you take an OTA update pushed by Verizon someday to update the ROM, that sequence would change. I am not privy to what all the characters really mean to those who know, but you may recognize G900V as the model of our Verizon S5.