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I will provide you with the direct translation first, and then explain a couple of things.
네, 제가 경상도 사투리가 아주 심한데,
Yes, my Kyungsang-do accent is very strong, so
일부로 안 쓰려고 표준어를 막 따라 하고 했었거든요.
In order to not to use it on purpose, I used to randomly repeat Standard Korean.
그래서 말을 할 때 "안녕하세요, 저는 OOO이에요." 막 이렇게 들으면 어색할 정도로 그렇게 표준어를 따라하곤 했어요.
So, when I talk, (in Standard Korean I would say) “Hi. I am so and so” I used to repeat Standard Korean to the point of being awkward if (you) randomly hear like that.
The use of 일부로 in the second sentence is wrong. It should be 일부러, which means "on purpose."
막 is a short form of 마구, and that means “at random” or “severely/badly/blindly.” The word, 막 was used as “at random,” in your sentences, but if it was used as “severely, badly, blindly,” in a sentence, the sentence usually contains a bad connotation.
Lastly, the subject of 들으면 (verb: 듣다 to hear) is "whoever" had to listen to the speaker's random Standard Korean practice. :)
Hope this helps.