Here's an update everyone. Soon after I started this thread, my phone's charging port totally died on me. It was probably a few days after the start of this. Anyway. I got a replacement Turbo 2 (seems to be in nearly brand new condition) and since this one came with the software version right before the latest one, I figured I'd test out the charging with this and compare it to whenever the latest update shows up on my phone. Hopefully it would be able to recreate the initial problem I had with my prior phone.
So, charging on the slower charger worked fine with the older software version so it was just a matter of time for me to wait for the current update. Update came today and I am pleased to say that all forms of charging, whether it be slow or rapid, is working perfectly!
My conclusion is that my charging port on my old phone was barely damaged enough to where it didn't show any ill effects on rapid charging, but was damaged enough that the slow charging was greatly diminished. And the coincidence of the software update and my charging acting up made me think it was a software issue. Glad it worked itself out!