Alright, I have solved the problem, and in case anyone else should run into it, well, this may be your solution.
First, to better define the problem: mp3’s in any folder on internal or external memory card would not work when set as a ringtone or alarm regardless of how it was set. Whenever the alarm/ringtone was called upon the system (specifically the app that called up the sound to play) would freeze and eventually pop up an error reading “Activity Media Storage Isn’t Responding”, which upon force closing would then work properly.
Now, various fixes did not work. Moving the mp3 to particular folders on internal or external memory did not work, for instance. Upon searching, it was mentioned on another Samsung model that this problem was related to the mp3 format and may be fixed by using the .ogg format. This alone did not fix it. Instead, the following process is what I did to fix it.
1) Convert the mp3 to ogg using whatever means you prefer.
2) Move the file into the root directory /system/media/ringtone or /system/media/alarm (/notification for notification). [Caveat: Using Solid Explorer to copy/paste the file did not work for me; it would say it copied, but the file wouldn’t work proper. Root Explorer, however, worked flawlessly. Remember to Mount R/W first!]
3) Change Permissions of the audio file. Permissions should be as follows:
Owner: Read, Write
4) Now, go to Settings in your ROM, find Apps, and track down Media Storage, choose “Clear Data”
5) Reboot and wait a couple minutes for things to repopulate.
6) When setting the alarm/ringtone, choose to pick the audio file via Media Storage, and your ogg file should be there. Voila. All should be well; the problem is fixed.
Now, does it have to be an ogg? I am not so sure, I took the ogg advice before tinkering myself and I didn’t try it with the mp3. Experimentation is how Newbie’s learn, you know, so go for it.
Admittedly, I did not Fix Permissions in Recovery this time, but I am certain I did in previous attempts to fix the problem. However, this is always a good first step.
Now, it seems I am the only one who had this problem, and I haven’t a clue why. If anyone has insight on that, well, I am happy to hear it because I’m quite curious about it. And in the off chance that someone, somewhere runs into this problem, on this phone or ROM or any other pairing, I hope this works for you as well as it did for me.
And, as always, thanks to the dev team!