I think it depends what you mean by acceptable.
I would say "no" generally to all three examples, with the exception of "must" and "should" in number one.
In cases of poetry, song, or if you were trying to be especially cryptic...or acting like Yoda or the Riddler, then these sentences would technically be grammatically correct.
However, in normal speech they would sound awkward and unnatural.
The exception would be:
Sitting on the stump MUST be a great big toad.
In certain cases the verb-noun inversion could be used to emphasize semantic differences between possible sentences.
Compare possible meanings for the change in word order:
"A great big toad must be sitting on the stump."
Possibility #1: It must be the case that a great big toad is sitting on the stump.
True(a great big toad is sitting on the stump).
"I think I see a great big toad sitting on the stump. I wonder if I am seeing it correctly." "Yes, a great big toad must be sitting on the stump."
Possibility #2: Concerning a great big toad's activities, it must be sitting on the stump.
A great big toad + True(is sitting on the stump)
or
constant (a great big toad) + variable(is sitting on the stump)
Example: "I wonder whether a great big toad would be swimming or sitting on the stump." "A great big toad must be sitting on the stump. It is too cold in the water."
Possibility #3: Of the many animals that can sit on the stump, it must be a great big toad.
True(a great big toad) + sitting on the stump
or
Variable(a great big toad) + constant(sitting on the stump).
Example: "Which animal is sitting on the stump at the tea party? A great big toad must be sitting on the stump."
Possibility #4: It must be the case be that a great big toad is sitting on the stump.
It is necessary that (a great big toad is sitting on the stump.)
Example, "In order to take the same photograph, a great big toad must be sitting on the stump."
Possibility #5: Of the animals that could sit on the stump, it must be a great big toad.
(A great big toad) is necessary for sitting on the stump.
Example, "If you want the top to look green, a great big toad must be sitting on the stump."
Possibility #6: Of the many things a toad can do, it must be sitting on the stump.
Is is necessary (to be sitting on the stump) for a great big toad.
Example, "In order to see how its legs bend, a great big toad must be sitting on the stump."
(six possibilities)
versus
"Sitting on the stump must be a great big toad."
Possibility #1: Of the animals that might be sitting on the stump, it must be a great big toad.
Sitting on the stump +true(a great big toad)
or
Constant (sitting on the stump)+variable(a great big toad)
Example: "There's something on the stump." "Sitting on the stump must be a great big toad."
Possibility #2: If something is going to be sitting on the stump, it must be a great big toad.
Sitting on the stump + necessary(a great big toad)
Example: "There are three stumps. How do I know which stump the path is next to?" "Sitting on the stump must be a great big toad."
(Two possibilities)
Note how the first way (with normal word order) can be interpreted more ways than the second.
Usually these semantic differences would be noted by intonation, with emphasis on certain words, but occasionally (such as in the case of a book, where the speaker does not have that ability) one might specify with the inverted word order.
"Sitting on the stump should be a great big toad" is acceptable, because in some cases speakers will repeat/state the given/constant of a sentence while thinking up the variable. It is sort of like buying time by saying "uh..."
The only other cases I can think of would be in sentences beginning with "there" :
There may be a chance that I won't go to the party.
There can be many people in one car at the same time.
There should be a door.
I think that this is not the same case, though, as use of "there" is more idiomatic...
For example, "a door should be there" does not equal "there should be a door."
in the first sentence, the speaker is indicating the location of a door.
In the second sentence, the speaker is indicating the existence of a door.
Does that help?