...Soooo, I thought my problems were gone, but apparently they're here to stay and then some.
After running my phone through two full charge cycles, I thought I'd try charging up my phone before it shut itself off, from like 40% or somewhere around there. It did actually charge all the way up to 100%, but this time around it stopped draining. Uh oh, problems again.
So, I had to go about the usual reboot/hard reset thing to see what my actual battery percentage was. Just like last time, occasionally the phone would reset itself around every 2-3 minutes. After draining the battery (which is much harder than I thought it would be, what with this glitch), I plugged it into my PC to let it charge and to back up the phone. Now, even as the phone is plugged in, it still keeps rebooting itself every 2 minutes. I then disconnected it from the computer to plug it into the wall charger, and the rebooting stopped, but now the battery percentage won't update again! However, the phone does recognize that it's charging, so I guess it'll charge, I just won't know what to capacity.
At this point, a replacement device doesn't seem too bad...