A small error in the second sentence
Correction:
I never ate meat.
我从来不吃肉。
No need to add "过"in the second sentence.
More examples:
我从来不撒谎。I never told a lie.
他从来不逛夜店。 He never went to nightclubs.
他父母从来不表扬他。His parents never praised him.
So you can tell from the above examples, "从(来)不+ V." is usually used as a past simple tense. It emphases that something never happened in the past. So if there is a "过"in this structure, which implies present perfect tense, it makes no sense.
Actually the first structure should be "从(来)没+ V.+过", (mind you there is a “过” in this structure), just as your original sentence suggests, it is linked to a present perfect tense.
More examples:
我从(来)没看过印度电视剧。
我从(来)没坐过过山车。
我从(来)没听过摇滚乐。