I definitely agree with the difference in formality.
> You should try and recalibrate your photon detector
I can totally imagine this, in a lab where all the equipment is old, and out of calibration, and the person saying it knows there are 10 other things that are more important, but this thing is still pretty bad and they feel obligated to point out the issue.
Whereas "try to calibrate" sounds to me like the process of calibration is quite hard and it's likely to end up no better calibrated than you started with.
It seems like you would say: You should try to recalibrate your photon detector
To someone who asks for advice.
“I can’t understand these results! You should try to…”
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.