The funniest part is using those exaggerated accents while speaking the language can actually help native speakers understand you better.
You'll always have a foreign sounding accent but the accent is part of the word so if your not at least somewhat faking an accent your not saying the word correctly.
You just gave me a flashback to an ESL class where one of my classmates was being a little shit, and decided to mockingly take on the most over-the-top English accent he could manage while reading aloud.
... Well it actually worked quite well and the teacher was pleased lol.
My "accent" is actually worse than that because I'm mixing up several American accents with British accents, with some scottish/Irish sprinkled on top. Plus my native french accent and the occasional German accent (because I learnt it before English and a lot of words are similar)