I get a feeling you took my wondering about the nature of these questions as "why the hell you care?". No, I was just curious, after all I used to ask myself similar questions when trying, and trying is the word, to get rid of my accent back in the day. Nothing this profound though, but still in the same "realm". So I thought that you maybe had picked up this same grand idea of losing your accent. It's not that I disapprove, quite the contrary actually and anyone who has managed to do away with their foreign accent would immediately earn my respect for what it's worth. In my abovementioned "trying" I did come to the conclusion that learning how to speak a different language native like is indeed possible, but that's such a complex matter that it's not really worth pursuing and is one of those things that can't be done on your own, you will absolutely need a lot of outside help to achieve this, unless you're some kind of uniquely talanted prodigy. Talking about how complex it is exactly is not really the topic in hand and it'd take a lot of page space to elaborate on it. Suffice it to say that even knowing what I was getting myself into having decided to try and get a good English accent, I never thought that there'd be so many obstacles on my way and it'd be way more than just learning how to pronounce sounds or even words properly.

Now it comes to that specific tiredness you mentioned. I think I might have experienced something similar if not the same, but the cause was a bit different, it was actually my little accent reduction quest. I've literally never undertaken a task with so many unknowns before. "Did I pronounce this correctly? I think I did, I did the right tongue movement after all. Let's record it and examine side by side with native speech. Ah... My voice is so different it's so hard to compare... If I only I had someone to consult with, to check my work. Blah, Blah, Blah..." All of that was driving me crazy, made me so nervous, antsy, eventually woozy. Not having a single tangible thing to grasp at was excruciating. After each instance of such study I felt like all around me was nothing but a long echo, I felt heavy headed, disconnected, all I wanted is to find something familiar that would help me put it all back together, return to reality. Now that I think of it, maybe it was not so different from what made you so tired. Both of us felt lost.

Anyway, that aside I can actually relate to inventing funny words and calling people names with it. It actually works like a charm, I used to do that when I was a kid. I think people's reaction to such stimuli is very natural though. People don't like things they can't understand, they're first reaction is like: "I don't know what it is, but it can't be good. Get away from me". Funny enough people actually quite often said this to a simple question like: "Do you even know what it is?"

- No! Shut up already

I guess this can very well be the reason for people not liking being exposed to speech they can't understand, repulsed even.

As for slurring some phrases. Well, just try to slur something that's not like a set phrase or at least something you can hear very often from literally everyone, a passage from some book for instance. I bet no one will really understand you, at best they'll have fragmented understanding. The human brain excels at forming patterns, then recognizing them, a database of sorts if you will. That's why we often see something familiar in some peculiar conjuctions of different objects forming an image to us. Like a big face on a mountain top, a sheep made of clouds etc... I believe it's natural that our brain functions like that, this imprints based logic can save a lot of processing power.