"My intuition is that this is found in a number of languages around the world" is a nice statement, but devoid of proof. I am looking for concrete examples in different languages.
I'm referring to vague memories of seeing these types of constructions in descriptive grammars. I'm working on a large comparative project of 300+ languages, and I've used multiple grammars for some, so I've probably looked over about 1000 grammars. I'm genuinely sorry I don't have notes about specific instances, but what I'm suggesting to you is that this is actually something that recurs around the world. I'd guess it's fairly rare, or at least rarely described, but of course that also depends on how grammaticalized you want it to be: it seems like Italian is more grammaticalized than French, and then both more than English (as in my notes above). If I do happen to see any of that again I can mention it to you. But all I can offer for now is some encouragement that if you look hard enough (honestly it might require skimming dozens or hundreds of grammars you have access to, online or at a library), you'll probably find similar examples elsewhere. However, if you are looking for concrete, detailed descriptions, that may not be the best approach anyway, because the sort of thing I vaguely remember is just a quite note (maybe half a page), rather than anything more detailed that you could use for a detailed comparative study. (In other words, using my approach you could probably identify a number of languages that have such usage, but not much beyond that enough to figure out specific variation within it.) You might simply be better off asking speakers of languages if they have constructions like that (as for French above), except that would bias your sample toward European and other familiar languages, whereas I'm suggesting you may find similar things around the world. Honestly I can't tell you that I've seen this
explicitly more than a handful of times, but remember that I wasn't looking for it intentionally. If I had to guess, I'd start with some African languages.
One relevant though vague connection I can point you to is that the verb "go" seems to grammaticalized as a narrative sequential device in some languages (a particularly good example is: Ebert, Karen H. 2003. “Come” and “go” as discourse connectors in Kera and other Chadic languages. In Zygmunt Frajzyngier, Erin Shay & Uwe Seibert (eds.), Motion, direction and location in languages: in honor of Zygmunt Frajzyngier, 111–122. Amsterdam: John Benjamins.
https://doi.org/10.1075/tsl.56.10ebe ), and then that similarly "go" is well-known to grammaticalize as an imperative marker (as well as "come"); for that, see among others Heine, Bernd & Tania Kuteva. 2002. World Lexicon of Grammaticalization. Cambridge: Cambridge University Press.
https://doi.org/10.1017/cbo9780511613463 (see "go > hortative") -- unfortunately that book does not have specific information about the type of development you mention.
"I've studied how conjunctions are used to combine imperatives and other verb forms". Can you provide any examples?
Sure. My dissertation is about
pseudocoordination where verb-and-verb constructions function unlike basic additive coordination. These are especially common in (but not limited to) imperatives. Typical examples in English include "go and get", "come and see", "try and do" (these function similarly to serial verb constructions, or subordination, etc.). So just while I've been looking for usage along those lines, I believe I have seen some things that would be of interest to you, but didn't take notes. (I've been working on this project for several years.)
If pseudocoordination happens to be of interest to you, I can share some of my work and additional references, but it does not generally include the type of data you asked about in a narrow sense. I'd also like to hear about the results of your research. Unfortunately right now I'm limited to just encouraging you to look for more information because I do think you'll find it, although it might be hard to locate or sometimes not too detailed.
Regarding the German (etc.) construction of incredulity that I mentioned previously, here's one accessible reference (and I might be able to find a few more if that would be helpful):
Zaefferer, Dietmar. 1990. On the coding of sentential modality. In Johannes Bechert, Giuliano Bernini & Claude Buridant (eds.), Toward a typology of European languages, 215–237. Berlin: Mouton de Gruyter.
https://doi.org/10.1515/9783110863178.215The author has made that available at either of these links:
https://www.academia.edu/1587801/On_the_coding_of_sentential_modalityhttps://www.researchgate.net/publication/332862299_On_the_coding_of_sentential_modalityAs for your explanation, it seems plausible, but once again you cannot explain phenomena which are not based on concrete data ...
Of course you're correct. What I wrote is based on my intuition from having surveyed similar meanings across several hundred languages-- very broad information, but not very detailed, and I wasn't looking for this specifically. Instead, all I'm suggesting here is that there seems to be an interconnected set of functions that are sometimes related by grammaticalization pathways, similar to the entries in Heine & Kuteva's
World Lexicon of Grammaticalization mentioned above. These probably occur repeatedly in different (unrelated) languages, although you can't assume it
explains anything in any particular language. To phrase that another way, I've made some casual observations that suggest relevant research questions (but not answers yet). And yours seems to be a good one, in that sense.
I hope that's somewhat helpful, or at least encouraging. I can't offer any specific examples beyond English because I'm not that intimately familiar enough with discourse markers (etc.) in the other languages I've studied. Certainly this doesn't seem obligatory for familiar languages (for example, I've studied Italian and can speak it at a basic level and this doesn't seem to be a salient or frequent feature [e.g. not mentioned in textbooks], but of course that's exactly why it's interesting and important that you're investigating it).