
Pinky
and The Brain...
I'm not 100% sure. I do believe that "mastering" a mix that's not quite the best it can be will bring out the worst in a mix, so it may be a combo of both instances. These might have been a bad mix to begin with, and bad mastering techniques or over-limiting. Also, if you're using free or cheap mastering software or plug-ins, they can also contribute to the harshness. I really doubt professional mastering houses use limiters they ripped from the internet. So, you gotta watch the final limiting for loudness. One thing that was suggested to me a while back is to use limiters in series. Instead of cramming the mix through one limiter set to kill, gently slide it through several limiter plugs with each one gradually increasing the loudness until you get what you want. That method works for me. I get decently loud mixes that still sound like my un-mastered mix - only louder. It's not drastically altering the sound. It's just louder. But if like you say, you were given tracks that may be of questionable quality when you got them, there's not much you can do about it. I'm a big believer in getting the source sound right. If it's right, then the song mixes itself and "mastering" is a breeze even with modest gear.
Agree about compression bringing out the worse in a track.

I think I'm following your idea, which I've seen applied in other ways but not to mastering. I may tinker a bit with doing a multi-stage processing on the final mix to see if that brings up the loudness without the squish. There's literally an entire science to compression and without having to go to studio school I'd prefer to find a simple, least time consuming method as possible to achieve a desired result.
One plugin I've been using for a while that I'm starting to get away from is cakewalk's original stereo chorus. Most of Mike's vocals I applied this, except nearer to the end of the album where I used a decent reverb plugin and in some cases applied no stereo chorus whatsoever. What plugins in what order is definitely an evolving thing. What I did 5 years ago I wouldn't dare do today. I also find getting the source where I want it saves me a lot of time later applying effects as well as EQ'ing etc.
Unfortunately I have zero budget to work with so what I accomplish is with what I have, so no preamps or studio quality mics. Maybe someday when I'm independently wealthy.

As for what you've heard on the Unenjoyment tracks, I did a listen on the way to the market just now. The car stereo is obviously one environment used for testing mixes. Cranked pretty loud it seemed balanced. I could hear all parts of the music clearly at all times. I hesitate to guess that your initial impressions might be due to choices I made in tone versus what you would have chosen to do differently. In the final analysis on the ride I'm back to start - it sounds the way I intended it to. Fundamental issue is that what I am aiming for may be slightly different than the audience wants or expects. To thine own self be true. I guess I'm still happy with it.