Ah, I remember the good old days when I believed that good presses meant good books and fancy universities meant good professors and PhD meant something other than piled higher and deeper. But then I got into the University teaching game: I was two and twenty and, ah, it's false. it's false. I had a book published in the same series as Chomsky's first book on transformational grammars and articles in a several prestigious journals. I went to conferences where famous profs from famous colleges said the most egregious things (one -- from Harvard even -- once gave a paper that was the clearest defense of a controversial position -- and then claimed forever after that the paper had totally demolished that position). And I sweated through years of grad school. only to find that the degree at the end was pretty much pro forma for endurance. The test of an idea is whether it works or not, not all the documentation that makes it look good or important or whatever. And, that being said, the muddle of agent and subject in your citations clearly do not work. any better than a cross between and orange and an earthworm.
But, the point I take it you want to make, that agent and patient (etc) can be expressed by many different constructions and appear, even in fixed SVO order, in many different orders, is surely true and not, so far as I can see, in dispute. The problems seem to arise from improperly mixing two different levels of language (three, if you throw in surface order), which you, following your text, see to have done regularly until this round, where you do it only once and that only by implication.
Set one: does have an object -- 'moku' in the second sentence. Interestingly, the first reading in this set is not the one intended but "the bird gets to eat. the beast gets foo. the bird eats"; the agent-subject connection kicking in wherever possible, as one would expect. But the intended meaning is also possible; it just takes context to bring it out (in this case, what the sentences are meant to be examples of).
Second set/sentence: no 'pi', since only 'soweli' follows. "Food works doggedly for birds" (same connection), on;ly context gets "Eating is what dogs do to birds"
Third. "Birds get to eat because of the beasts" (vultures?)
Fourth. "Birds get to eat because of the beasts' eating" (remora of the bird world?) I'm not so sure about this one having the structure you suggest, but it is in the right direction, I suppose.
Fifth. Possibly not good tp, but we need to know about what can happen before 'la'. And, it doesn't obviously mean what is intended; it needs an 'ona' to tie the prenex in.
Seventh. No. The 'en' is either a logical "and", which means we could split into two sentences identical but for the subject, or a communal "and' which means that the two do the whole thing together, which is clearly not what is meant here (one eats, the other is eaten, but there is no one thing they both do).
No one (except possibly your author) says that S and A or O and P, have to line up exactly. The best you can get is a statistical connection -- which has a psychological reality, as the first readings of the above sentences suggest. The crucial point is that they are two different categories (which your author seems not to know) and the various ways that the one (A-P) can be expressed in terms of the other (S-O, various oblique devices) is a matter of all the stuff that lies between, including, as you note, stylistics.
As for numbers, the only sensible thing to do -- as a proposal rather than a jeu d'esprit -- is decimal place notation (maybe more later at the other site).