Hi Mitch,
I can already hear the grumblings about how metalanguage is the problem here, so note my purpose is not to explain or defend it. You are using the terms I defined at the outset of the essay, but do not expect them to be universally understood or adopted here. The key question I was trying to address is how to differentiate, or better yet *track*, when an author is building out and elaborating on one main idea versus moving on to a new idea. This approach assumes that there are multiple levels in a discourse, so one might be answering this question at the pericope level, within a pericope, or even within a clause.
Another thing to keep in mind is that my paper was not written with books like 1 Peter at the forefront, which (at least by NT standards) have a much lower ratio of finite to non-finite verb forms compared to say Luke or Peter. I would suggest that where the latter rely more upon conjunctions and relative clauses to create dependency relations, books like Peter more characteristically employ non-finite verb forms to create larger, complex dependency relations.
In both cases, however, the purpose is the same: to take what might have been a series of seemingly equal verb clauses and to cluster them into one complex whole, centered around one main clause on which they depend. For example, Paul uses connectives and relative clauses in Eph 1:3–14 (along with non-finite verb forms) to create one complex thought through use of grammatically dependent relations. We might well need to translate these into English as a series of finite clauses, but the exegetical point remains: Paul's choice to employ these dependency relations suggests intentionally shaping them into a larger complex. The same would hold true for 1 Peter 2:13 ff, only the author uses a different ratio of these dependency markers to accomplish much the same effect (more dependent verbs and fewer dependent connectives/relative pronouns). While the traditional grammarians might advocate translating some of these participles and infinitives as finite verbs, a close reading of their caveats generally reveals a recognition that use of the dependency markers served a structuring purpose, regardless of translation to English.
Mitch Tulloch wrote: ↑February 25th, 2018, 1:06 pm
I've been trying to read through 1 Peter and I was wondering about the "sentence" 1 Peter 3:7 which has no main verb, only participles and an infinitive. So if the verse is a "support clause" as per Runge's chapter then what's the "main clause" of Peter's "theme line" here? I almost think it must go way back to Ὑποτάγητε...διὰ τὸν κύριον in 2:13 since the whole passage 2:13 to 3:7 seems to be based on the idea of submitting to the Lord (or in the case of husbands, submitting to the idea that they should be considerate towards their "weaker" partner). But that kinda makes the grounding structure a bit more complicated than the simple indented examples Runge shows in his chapter!
Indeed! 1 Peter 3 is not discussed in my paper, so this is you "going rogue" to try and apply the principles outlined to a tough section of text!

I have a chart for this section of text (see below) that attempts to represent the systematic embedding of supporting elements, all centered around the most likely governing verb in the context: the imperative ὐποτάγητε in 2:13. Some here will disagree with the need for such a claim, but the framework I'm using demands an exegetical accounting for the grammatical choices made. On my view, the reiteration of the same verb in the form of a participle ὑποτασσόμενοι effectively signals that the points begun in 2:18 and 3:1a are still contributing to the same overarching theme (and grammatically governing finite verb) of 2:13.
This raises the question of what is happening at 3:7a based on the fact that we have another participle but a different lemma. Does the use of a different lemma mean the beginning of a new section, or does the use of another participle (and form of direct address "husbands") in parallel to the others mean it is extending the complex elaboration of 2:13? I believe the answer to both is "yes," but the critical question is how one prioritizes the two. Which comes first?
On my view, syntactic dependency is most naturally processed as the higher-order governing constraint, viz. that 3.7a is another dependent action elaborating on the main idea of submitting to every human authority of 2:13. Thus, the complex cluster begun in 2:13 extends through 3:7, in my view. The change in lemma from that repeated in 2:18 and 3:1a is attributable to the author wanting to address a key point under the same discussion that was not entirely parallel, but rather represented the other side of the coin for 3:1a. The use of direct forms of address (slaves, wives, husbands) further supports understanding this as a third parallel application, but slightly different based on the shift in lemma.
Think of the alternative options. Had the author used a full imperative form at 3:7a (συνοἰκεῖτε), it would more likely have been understood as parallel to 2:13 based on the verb form than as parallel to 3:1 based on the parallel use of direct address.
Here is the charting based on my understanding of the dependency relations. One would need to read the article to understand the representation, so I don't expect it to be immediately obvious to everyone, nor do I intend to give a blow-by-blow working through it here on the forum to defend it. The {2:13} nomenclature is meant as a reminder about the governing verb form, i.e., that when the reader read a participial repetition of the governing imperative, it is reasonable to assume they would have placed what follows under the same thematic umbrella rather than understanding it as an "imperitival participle." The latter stems from English not really supporting this level of embedding using dependent verbs. We'd more naturally use dependent conjunctions with finite verbs.

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One key thing is how to take the imperatives of 2:17. On my view, the passage makes most sense if they are understood as continuing the comparative ως section of 2:16. If not, then what I understand to be the elaborating participles of 2:18, 3:1 and 3:7 need to be construed as elaborating on the exhortation of 2:17d or as imperatival participles that somehow stand on their own, both which are problematic on a number of levels.
Another clarification is that the purpose of the chart is to help students synthesize the implications of grammatical decisions made at each of the different levels into a holistic reading of the text. I am NOT claiming in any way that it represents precisely how an original Greek speaker would have structured things. The goal is to trace the implications of the various decisions in order to trace the flow and development of the author's argument. This is the current evolutionary point of development.
I wish I had a nice methodology monograph or paper to point you to to better explain this charting strategy, but the non-narrative paper you cite is as close as I have gotten. I still am learning too much to feel comfortable waxing eloquent about how things work. The more I read, the more messy language I encounter that challenges me to nuance and adapt. Hopefully one day we will have a representational summary like this, something related to—but different from—syntax trees that will help us summarize the flow of a writer's argument based on their grammatical choices.