Oftimes, particularly with verbs, I approach definitions as mathematical equivalents, as in, since y = 2x, 2y-5 = 2(2x)-5.

[one should] = [the best course of action is to]
one should not = the best course of action is to not

However, commutative and distribution laws appear to not apply.

to not [verb] ≠ not to [verb]
one should not [verb] ≠ the best course of action is not to [verb]

Am I being far pickier than the rest of the world?

The difference in, for example, "to not apply" versus "not to apply" is minor but distinct to me. But it seems most English speakers don't perceive one (especially in light of rules about splitting infinitives, which likely came about because it isn't possible in Latin, so one should avoid splitting infinitives when translating from Latin to English).

"To not [verb]" = "to actively or consciously avoid [-ing infinitive verb]"
"Not to [verb]" = "to do anything other than [verb]"

The former is more active and the latter is more passive.

I wonder how much of this is influenced by the first years of two foreign languages, particularly Latin, where my instructor was also the AP English teacher.