First of all, let me congratulate you on the eye-watering number of cannons you are aiming at this particular Mosquito!
A few things are interesting here; the mixed tense, the way that the 2nd verb can optionally split "came out" ('He came shuffling out' = 'He came out shuffling').
I'm not sure if some of that weirdness helps highlight or obscure the things going on in this sentence.
{Before I start, I should say I am not a grammarian, and only believe in grammar to the degree that it enables semantic value. So if I make an obvious mistake, feel free to edit or condemn as you see fit.}
My suggestion is that 'Path Verb plus Manner of Motion Verb in the Ing-Form' is a very specific instance of Attributive verbs (or Verbal Adjectives)
This paragraph in particular seems to describe what we see here:
"The truly "verbal" adjectives are non-finite verb forms: participles (present and past), and sometimes to-infinitives. These act as verbs in that they form a verb phrase, possibly taking objects and other dependents and modifiers that are typical of verbs; however that verb phrase then plays the role of an attributive adjective in the larger sentence."
What is particularly meaningful about this way of looking at it, is that it explains a quality that none of the other options seem to address. The two verb phrases can have their relationship and tense inverted, and the sentence still works.
"He came shuffling out" = "Coming out he shuffled" = "Shuffling he came out" = "He shuffled coming out"
With those adjustments you see that each verb is equally ready to act in support of the other. They are not complementary or elliptical, they are parallel; neither refers directly to the other, but both refer concurrently to "he".
The tenses can also be modified to match, without causing syntactic or semantic harm. Which helps to emphasize that this is not an adverbial relationship.
"Shuffling he comes out" = "He comes shuffling out"
You also notice how multiple verbal actions can behave adjectively describing whatever the target of the primary verb is.
"He came out shuffling, drooling, and verbing like a madman."
When you start viewing "concurrent verbal phrases" in terms of working like adjectives you notice that it avoids the traps you outline for the other 5 options, and works in a manner that is consistent with the larger structure of adjectives.
What's particularly interesting is that verbal adjectives aren't really common in English, but are standard in other languages.
(I'd like a good citation for this, but googling only seems to provide a lot of anecdotal evidence. So here is a sample of that: http://lughat.blogspot.com/2009/01/verbal-adjectives-in-english.html ) I suspect that, in English, we are more likely to address that particular language function with various forms of clause parsing; so you may only see English Attributive verbs in short sentences.
( This theory once tested, searchingly; might validate that English tends to resolve this need by using, preferentially, adjectivized forms of verbs.)
{Edit to clarify a bit further}
The original poster asked if this represents a disagreement with this quote from the thesis "In sentences (26) and (27), the verbs in the ing-form clearly define the way of movement. On the other hand, the ing verbs in sentences (28) and (29) are participial clauses denoting simultaneous actions"
Yes, and no. Mostly I think it's a missed opportunity for the author. They hint at a thin line but don't actually define where it is.
The structure of samples 28 & 29 highlight the participle usage, enough that they are easily definable as separate clauses (they came in, they were chatting, they were laughing).
Let's examine it further by looking at it in a restructured way, "the women would come chatting and laughing in". It just feels wrong; but there's a genuine possibility that it isn't.
This sample shows that we can split come/in by more than one participial clause without it feeling as wrong: "the women came singing and dancing in".
Clearly the "kinetic aspect" of dancing has an influence that helps. We're more comfortable with "came... dancing in" because both clauses work equally with "in". (she came in, she danced in)
Does it have to be a kinetic verb? Consider this phrase: "The crowd stood when the team came cheering in."
Something in that sentence might snap at us, but it works syntactically and semantically.
So verbs that work in a Path & Direction method seem to have an influence on how willing we are to lump attributive verbs together. (Perhaps because we're subconsciously saving ourselves from repeating the directional item for each separate clause.)
So I would disagree if the author implies that the samples are different grammatical types, but I would agree if they are saying that "Path Verb...etc" works as an effective probabilistic tool for finding Attributive Verbs that we treat in an entirely undisguised manner.
Best Answer
You are confusing adverb(ial phrase)s with objects. In your example sentence
The new arrivals did nothing to the classroom that would make it an object of the action. Both "at the classroom" and "with only seven seconds to spare" are adverbial phrases. They refine the action described by the sentence, explaining where the subjects arrived and when. These are two of the major categories of adverbs. Some of the other categories are words or phrases that describe why or how the action occurred:
There "loudly" is an adverb, and "at the joke" is an adverbial phrase.