To begin, I want to express, in summary, that I feel the two sentences have the same meanings because "difficult" has two senses. Differences in "to not" and "not to" can be very subjective. Ordinarily, it takes a lot of imagination.
I spent a lot of time mulling over this question, until someone walked me through a guide on figuring out parts of speech:
- Start with the verb (to become famous; to have a goal).
- Move to the adverbs (not). That's far enough.
And that's where I came to understand the difference between "to not" and "not to".
- I suggest we start with an easier sentence pair: "I told him to not go."; "We told her not to go." This will be very easy to express.
- It's easy to think of "to" as synonymous with "until" or "until ~ happens".
If you cycle the synonym into "I told him to not go," you get "I told him until he didn't go." In this sense, it's more invasive. The subject continues its action until the indirect object ceases its action. It's a very condescending and controlling action.
If you cycle the synonym into "We told her not to go," you get "We told her not until she went." The difference is austere! In this case, the indirect object always has the liberty to complete its intended action, but the subject continually "disapproves" until that happens (perhaps with the hope that things will change).
Getting back to the "part of speech", we can see that "not" is an adverb. In "to not", the adverb is post-prescriptive. In "not to", the adverb is pre-perscriptive. But "not" is very abstract. It's easier to use an adverb that can be easily visualized, "jovially":
- I told him to jovially go.
- We told her jovially to go.
It is clear that jovially in case 1. modifies "go" and modifies "told" in case 2.
Back to the sentences in question
- "It's difficult not to get that feel-good mood." -and-
- "It's difficult to not get that feel-good mood."
In 1., "difficult" is actually transitive and amended with a zero-object and should be "hard [for me]", means 'hard':
In 2., "difficult" means "negative"; therefore, the sentences have a shared meaning.
- "It's difficult for me not to get that feel-good mood."
- "It's not to not get that feel-good mood."