I grew up in the Southeast, and this usage is common. Both in Southern accents and AAVE.

I agree with skrebbel's feeling about the phrase, and I think yours is also a little bit correct.

To add more character, I also think "try and" feels more casual and friendly. Less like a technical suggestion and more like a form of encouragement. More caring, less distance or annoyance.

"You should try and get some sleep. [I care about you, you poor thing.]" vs "You should try to get some sleep. [Why are you still awake?]"

There's more closeness with "try and" and more distance with "try to".

"Try to" feels formal, technical, distant. "Try and" feels comforting, compassionate, friendly, but definitely not something you'd use for a complex task.

I couldn't imagine "You should try and recalibrate your photon detector" ever being said.