Yeah, maybe it's regional. I hear "tryan get some peace and quiet" about the same as "tryta get some piece and quiet. Maybe the former is more confident. But tone of voice probably matters more than the words.
FWIW I grew up mostly in the Northeast.
I concur with "tryan" - it's its own word, IMO, in my mind. I had never seen "Try and X" sentences written out before this article, even though I say "tryan" all the time.
I'm surprised there was no mention of accent. For their example "It’s tough when you’re trying and finish(ing) an assignment under pressure.", I can't help but hear "It's tough when you're tryna finish an assignment under pressure.", which really is more like "trying to" than "trying and finishing".