If you took away "literally" in both cases, it would still be understood to be figurative. "Literally" isn't doing its job of meaning literally, but it isn't meaning figuratively.
I think the correct understanding is as hyperbolic use of the regular sense of literally.
If I say, "I walked miles around the store looking for you" or "I waited for you for days", we don't say "sometimes miles means hundreds of feet and sometimes days means a few minutes". We say people sometimes exaggerate.
In the same way, "Tom was rolling in wealth [so much so that it's almost as if he were literally rolling in wealth, but of course that interpretation is silly and I'm using hyperbole to exaggerate how rolling-in-wealth Tom was]".
I don't understand the distinction you're trying to draw here. Literally 100% of the time modern people use the word "literally" in a way that means "figuratively" it's to engage in hyperbole but it's also to explicitly mark that what follows is not to be taken literally.
As you say, you can engage in hyperbole without marking it.
The distinction is that you cannot substitute the word "figuratively" in these examples, because it does not mean "figuratively".
If I say "I figuratively am going to kill him", you're highlighting the figurativeness of the act. You're stressing that you're not actually going to kill him. The meaning of the sentence is "I'm going to kill him... but not really".
If I say "I'm going to kill him" or "I'm literally going to kill him", which mean basically the same thing, it's still implied to be metaphor. But what's being stressed here is the closeness to the metaphor becoming actually literal. The meaning of the sentence is "I'm SO angry with him that I'm ALMOST at the point of killing him".
It's subtle, but there's definitely a distinction. "Figuratively" is a dehyperbolization (it's not really gonna happen), "literally" is a hyperbolization (it is hyperbolically really close to happening).
I think the correct understanding is as hyperbolic use of the regular sense of literally.
If I say, "I walked miles around the store looking for you" or "I waited for you for days", we don't say "sometimes miles means hundreds of feet and sometimes days means a few minutes". We say people sometimes exaggerate.
In the same way, "Tom was rolling in wealth [so much so that it's almost as if he were literally rolling in wealth, but of course that interpretation is silly and I'm using hyperbole to exaggerate how rolling-in-wealth Tom was]".