I see the issue - it looks like it could be a "～って(いうのは)いいぜ" kind of construction. But in that case the preceding bit wouldn't be te form, it would be "動きやすいっていいぜ" or whatever.

Rather, the っ here is just an affectation that makes the speech sound a bit childish. What's being said grammatically is just 「動きやすくていいぜ」.

I think you're correct about the two statements not being completely independent, though. In both the shorts and backpack examples the second adjective is meant as a corollary of (or subordinate to) the first. タンパン（は）よくて動きやすいぜ！ or このリュックは便利で大きい both sound unnatural and it seems to me like the logical relationship between the adjectives is lost. The same grammar could technically be used to combine two independent statements, but the context indicates the (pseudo- ?)dependent interpretation.

In English we would just say "Shorts are easy to move around in!" and it wouldn't lose any of the semantic meaning, but I do think TFA's "nice and easy" might preserve some of the "feeling" of the Japanese without sounding unnatural like a word-for-word translation would be.

I'm not a native speaker though so I could still be completely wrong.