The simple fact is that Sonja proper has not said a lot in a long time, though things are starting to turn up in the notes on this site. Much of what is set in at least silly putty is from jan Pije's lessons, whose status is about as official as it gets, for the most part. Everything else is balls in the air in the forums.
As a general remark, it is probably important to keep separate discussions about stative verbs (and adjectives) and active ones, since they behave differently in many cases. Handily, the transitive forms of statives are all active, but that means that, if the object is missing, the form becomes ambiguous: 'mi pona' can mean "I am good" or "I am improving (myself)" and so on. (Of course, the case with active transitives is worse: 'mi moku' can mean either "I am eating" or "I am food".)
A couple of times you seek to resolve problems by sticking 'lon' in. I don't see how that helps; 'lon' is not hardly (oy, the problems with negation purIsts!) ever a translation of English "be" but mainly of English "at," so 'mi wile lon sama sina' means something like "I want to be at the same place as you"
In general, modals are defined as verbs that take verb phrases (including, perhaps, DOs and prep phrases) as complement. The clear cases are 'ken' and 'wile,' with 'kama' as a case which seems to need some special attention (but I am not sure why).
On the differenvce between 'tenpo kama la mi toki' and 'mi kama toki,' I tend to see possible subtle differences (between future tense and inchoative aspect, say, or between prediction and intention), but I am not sure there are really any such. There are, Lord knows, problems enough with the simple modal use (maybe why there is a special section on that in some cases). Take 'mi kama moli': as a simple prediction (or future tense in general) it is clearly true --and that fact is probably clearer stated as 'tenpo kama la mi moli' ("At some time to come, I am dead" -- 'moli' is stative, not active). But it also marks a change of state. "I am dying," even "have just died" (implausible in the first person, admittedly).
'lukin' (from Sonja) and 'alasa' (elsewhere) are meant to be for "try to," not merely future (or even future)
'kama lon e kili' means "come to place a fruit," i.e., put a fruit in some place, NOT "come to be a fruit." ('lon' = "at", =/= "be")
'pini' and 'weka' in your examples suggest another famous problem: stopping, quitting and finishing. States just stop, as do some activities, while one quits others, but still others (processes, to add yet another technical term) stop or one can quit them or one can finish them and, if one quits them or they stop, they can start up/be started up again (often where they left off). These are also the thinks that one can undo. generally. How all of this fits in here, I a don't know and don't have any thought out suggestions how to proceed. I just have fifty years of fiddling with all the ins and outs of them, so am ready to make pointed comments about just about any suggestion. Sorry 'bout that. Incidentally, most activity words are ambiguous between the two sorts and also have stative uses. Oh, joy!
'mi ken' needs a lot of context, but generally means "I am fit" (for whatever is in the offing). I also means "I have my rights" but that takes a very political context to come out.
'mi kute' also means "I can hear' (the "can" here is an English usage -- indeed SAE -- that escapes rational explanation). similarly for 'lukin'.
'mi mama' makes more sense as "I am a parent"
'mi moli' strictly means "I am dead" but in the first person has to take on other implications.
'mi lete' is "I am cold" ("I am sleeping" -- again odd -- is 'mi lape')
'mi musi' also means "I am entertained" (just as 'mi moku' also means "I am edible")
'mi olin' means "I am in love", the transition goes to 'kama'
'mi pilin' also (and more naturally) means "I think" (tan ni la mi lon).
'mi pakala' more likely means "I am destroyed"
'mi pini' doesn't obviously flow over to 'moli' nor even "done for"
'mi seli' means "I am hot" Now, here, as in many other of these cases, there may be an implicit possibility for a hidden reflexive DO. That surely happens sometimes (with 'tawa', for example) so it may be general and that needs to be explored.
'mi sama' This is hard to imagine context free, other than as a response to someone saying how they are. Your interp is not very plausible, even with a hidden reflexive DO.
'mi seme' is just "What am I?" a perfectly common question. I wonder what this list is all about, by the way.
'mi sona' is "I know (missing DO)" or "I am wise"
'mi suli' is "I am big"
'mi suwi' "I am sweet"
OH, never mind. I see that these are not intransitives at all, in your mind, but transitives with unexpressed DOs, which are often (but not always) reflexive and otherwise indefinite. But then you wander off into other things, so I just don't understand after all. Sorry.
'mi wawa' = "I am strong" nothing more fancy. Maybe (but how likely?) "I am exercising" which would involve some flailing and the like probably.
'mi wile' "I am needy" "I am willful"
Both 'mi moli e mi' and 'mi moli e sama' mean "I kill myself" with what shades of difference I do not (yet -- because no one has played around with this) know.