I think you are overly pessimistic. As for predicates (what comes after 'li') you have
nouns that stay nouns (unless transitivized -- in which case they mean "makes object (after 'e') be a ...")
modifiers that stay modifiers (unless transitived -- as above)
verbs that stay verbs (change slightly when transitive, or, more likely, when intransitive)
prepositions disguised as verbs ('tawa' class take nouns as complements)
modals (take verb predicates as complement, 'wile' class)
'kama' that is somewhere in between (takes modifier and noun predicates, but not noun complements and lotsa other strange stuff)
All of these can be modified adverbially, nouns and modifiers also by nouns and modifiers. And 'ala,' which does its own thing.
The tricky part is to notice that the grouping of all these critters is different for modifiers and for complements.
Sorry, that just looks worse than before. but it is easy, once you get the hang of it, though hard to put into words succinctly. In any case, a given word doesn't enter into so many grammatical possibilities -- most have only one or two, and the worst I know has like four, usually clearly distinct (but, when not, doozies).
This information is interesting to me. Well, 'sona ni (borrowing your form) li namako e mi' 'li musi tawa mi' (not sure about that, but I think that is how the pieces line up, though 'musi e mi' may work , too). The crucial point is that the object of 'sona' is some mental thing, either what you know or what you mean, not you yourself.
depending on what the rest is 'wile kama tawa moku' can means as little as "wants to come to dinner," than which we can surely find something more complex. I like "wantsto become a ravening rover" myself.