Locative Inversion in English

Hi.
I'm a Japanese university student, working on my graduation thesis.
I'm studying locative inversion with modal auxiliary verb, such as (1-3).
(locative inversion consists of <locative phrase+verb+subject>,and
its derivative <ing+locative phrase+be+subject>, by my definition. )

(1)Sitting on the stump {will/ may/ can/ should/ must} be a great big toad.

(2)In the caves {will/ may/ can} hide a fierce lion.
(3)Down the hill {will/ may/ can} roll the baby carriage.

Are these sentences acceptable?
If you think acceptable,
which modal aux will be a top, and which will be a low?
If you think unacceptable, what contexts are required to make these sentences acceptable?
(As for (2) and (3), a sperker or writer who states (2) guesses a present situation,
and a speaker in (3) guesses a future situation.)

I have a poor intuition to English, so would you be my informants?
Of cource, I don't mind your answering my questions according to your feeling!