Why you’re wrong
What's going on here might become more apparent with the verb “eat”:
Hopefully, I’ll eat some of that chocolate.
“Hopefully” doesn't seem to make a lot of sense as a modifier for “eat”. You might eat quickly, eat sloppily, eat slowly, eat languorously, eat voraciously, or eat piggishly. I think you could even eat angrily or happily. But it's hard for me to imagine eating hopefully. The only way I could imagine eating hopefully is during a religious ritual like the Eucharist, where you might hope that the cracker, while you are eating it, is really, truly, and substantially the body of Christ. But that's not what one ordinarily means in a sentence like the example.
The intended meaning is:
I hope to eat some of that chocolate.
or, to spell out what's going on very explicitly:
I hope that the sentence “I’ll eat some of that chocolate” is true.
Why you’re right
On the other hand, there is a reasonable argument that this kind of sentence can at least sometimes make sense both ways. Another of your examples could be understood like this:
The chocolate was many things: brown, sweet, bunny-shaped, and out of reach. The chocolate's possession of the bunny shape—that is, the connection, or shall I say, copulation,* between the chocolate and its shape, which we commonly denote by the word “was”—was unfortunate, but the chocolate's possession of ‘out of reach’, if you don’t mind my sounding like a Scholastic philosopher, was fortunate.
Of course, “if you don't mind my sounding like a Scholastic philosopher” referred to the whole clause, not just “was”. Or, uh, maybe it referred to both, in a way. Where’s Jean Buridan when you need him?
The moral of the story
The moral of all this is, sometimes it doesn't matter whether you think an adverb is “sentential” or whatever grammar jargon there is for an adverb that modifies a verb but not the sentence as a whole. Or a clause as a whole. Or whatever.
English doesn’t care. English doesn’t provide different forms for adverbs that modify a whole sentence vs. adverbs that modify only the verb.
English does care about some weird things, like what time it is or whether the relevant instance of a noun is already present in discourse. English demands that you make choices about those things whether you want to or not, by choosing a tense for the main verb and choosing an article for every noun. (Having no article is still a choice of article—a hard thing to learn for people coming from languages without articles.)
But English doesn't require that you indicate your choice about whether you intend an adverb to modify a whole clause or just its main verb. English gives you some ways to strongly suggest one or the other, like where you place the adverb in the sentence and whether you surround it with commas or pauses, but ultimately the reader's common sense will determine the right interpretation. In most cases, only one interpretation is reasonable, in which case everything is fine. In some cases, one could argue that both interpretations are reasonable but it doesn't make any difference. In those cases, it doesn't make any difference—and English doesn’t care. Maybe you can think of a sentence where both interpretations are reasonable and it does make a difference. That might make an interesting question for ELU.
* Most dictionaries don’t list it, but there really is established usage for this meaning of “copulation”. See the OED, sense 1b, which is not even marked obsolete. Just don't say you learned it here.