I generally think the rule on splitting infinitives was made up by English majors upset that English isn't more compatible with Latin, but in this case I think the attempt to avoid the split made the sentence weaker and ruins the sentiment.
"Trying to not kill yourself" implies effort. It sounds like you're actively avoiding something. "Trying not to kill yourself" sounds like you're doing something different, to change it up.
You're right. There's no actual rule in English that you can't split infinitives. It was copied over from Latin in an attempt to try to come up with some rules for grammar.
Source: Many nerdy discussions with Star Trek geeks about "to boldly go where no one has gone before"
That’s interesting. I feel differently. “Trying not to kill myself” sounds a lot more natural than the split “trying to not kill myself.” “Trying to not kill myself” sounds like internet slang that makes the statement sound awkward on purpose so it’s taken less seriously. But the former format is way more natural to speak.
This might be a regional difference, but when I say it out loud, 'tryna not kill myself' is by far the more natural construction. But I agree that in writing, 'trying not to kill myself' feels more natural, while 'trying to not kill myself' feels stilted and intentionally awkward. Man I love language.
I think there might also be a subcultural difference, too, because there are different types of “tryna” that are used by different groups of people, and maybe being used to a more versatile “tryna” would make “tryna not x” more natural to speak.
Tryna A: “I’m just tryna screw in this lightbulb,” “I’m not tryna hurt you”
Tryna B (expanded tryna, not spoken by everyone, mostly skews younger and bro-ier I think): “You tryna go to Taco Bell right now?” “You tryna chill tomorrow?”