[Verizon Galaxy Note 3 Q&A, Help & Troubleshooting] verziehenone:
Sorry to hear that! I know i've seen other reports on the interwebs saying similar things, but did not see any threads with discussions about theories or investigation, beyond the 'me too' I see often (which is entirely fine, and unfortunate for those who also have this issue!). Having the volume helps a ton, but i'm surprised I didn't see more analytical or critical thinking / discussion happening in the many threads, and figured i'd just get the ball rolling and hope this helps others (even if it's just mostly me putting findings down).

That said, I have more information to offer.

1) Alarm - Day 1, following the Factory Reset yesterday, it started without issue (not unexpected). I expect that the issue (if it does) will re-appear sometime around Friday - Saturday.

- Other than installing some apps (as mentioned previously) mostly things like Netflix and some games, I have not installed anything that (from what I can see) should interfere with an Alarm app

- I am presently using Alarm Clock Plus (the second of two apps I encountered the issue in); this is for consistency, and also because the app worked without issue for over a year prior to this

- I have not 'Turned off' any apps, though previously (prior to the Factory Reset) I had turned off some apps mentioned in other XDA threads as not required by the system to run (mostly Verizon and Samsung apps)

- I am not and have not rooted this phone at any time; this is 100% stock Android at this point (well, as Stock as a Samsung phone gets)

- After speaking with a few friends, they have confirmed that: this issue has occurred with the stock Alarm Clock app and another 3rd party app (one I have not tried yet) as well; but one friend has not experienced any Alarm issues at all (though he may just not be aware of them, so i'm taking his account with a grain of salt)

2) Music - To add to my previous notes about the issue around the equalizer ..

- I am able to (as indicated previously) re-create the issue on-demand by scrubbing

- I can re-create the issue relatively reliably by hitting 'Pause / Play', and I didn't see a difference (in ability to reproduce) whether it was from the lock screen or in the app that I hit 'Pause / Play'

- It does appear that (with inconsistent results) I experience the Equalizer turning off / on by itself, if I keep listening to songs the issue seems to reverse. (i.e. Song 1 is fine, Song 2 - Equalizer turns off, Song 3 or Song 4 - Equalizer turns back on) I encountered this just a bit before this post, and sure enough, after hitting 'Pause / Play' I was able to verify that the Equalizer had turned back on.

- I am now 100% positive it is the Equalizer being horked by the phone / OS / something. This is based on replication of the issue (where it sounds like it gets soft) being the exact same sound as when the Equalizer is just turned entirely off.

A few things to test today / next few days:

Alarm issue:

-None at this time; keep observing

Music issue:

- Google Play Equalizer app (see if issue occurs still outside of the stock Equalizer)

- Try non-Cached music to see if this is a factor (including 'Pause / Play'; song scrubbing; etc)

- Try an alternative to Google Music (this is not a practical solution to me, but would provide comparison data)

Last note:

- After completing the Factory Reset and hearing my story yesterday, the Verizon rep did inform me that I could bring the phone back, if the issue keeps happening, and exchange it for a refurb. I'd rather avoid this if possible, as I feel like i'm not as confident it is a hardware issue as before, but this is an option (and may be an option for others wishing to try this path). Obviously, I hadn't rooted, so the Manufacturer's Warranty was available, so YMMV.