I'd describe it as:
- "try and" implies that the reason for failure is slightly more likely to be from laziness / not actually attempting it
- "try to" implies that the reason for failure is slightly more likely to be from incapability
As in:
- I'll try and kill the mosquito... that has been annoying me all day
- I'll try to kill the mosquito... but it's quite hard to hit with this gun
But nobody would notice if you used the wrong one.
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.