"Swinging the world by the tail" is a pretty common colloquialism down here in Bubbaland, and "swangin'" is probably nothing but a take on southern US diphthongization. From a linquistic standpoint, the "a" sound in "swang" is not a single vowel sound at all, but two sounds, one of which slides into the other. No self-respecting Southerner will ever use just a single vowel sound in a word if there's any way to squeeze in two or three. I have often heard the name "Bill" turned into a three-syllable word by my Alabama neighbors. It goes something like "Bah-ee-ull".

Another word which undergoes the same transformation as "swing" to "swang" is "pink" to "pank". Of course, there are those of us who believe that there is a definite difference between "pink" and "pank". I shade of pink that appeals to you is "pink" while a shade that is gaudy, gauche and obnoxious is "pank".