Is it appropriate to rewrite and republish another author's useful but very badly written paper? I found an engineering-related academic paper from a number of years ago that was published in an obscure journal, likely not peer-reviewed. The English writing is very bad, like it went through three languages in google translate, and many key parts are nearly incomprehensible with awful grammar and incorrect word usage all over. Organizationally it's rather a mess too.  While it took me quite a long time to decipher it all, I recognized the value and importance in it, and I think should be more widely seen, as there is really nothing else published on this specific topic.

I was interested in potentially redoing the paper to better present and explain the ideas in it. I would want to add my own ideas of interpretation and application too.  I wrote to the original author and they responded, and I think they'd be ok with the project? I couldn't discern a clear answer from them yet.

In the sense of academic standards, what is appropriate in this situation? Is it acceptable in the first place to redo and republish someone else's full work? Do I become a new co-author, or simply an "editor", or new main author while at the start somehow noting it's a rewrite?  Or where is the threshold between plagiarism and a newly written paper if I redo it from scratch, but following and using all the original author's ideas and data, and then add my own thoughts?  I really can't maintain any of the original written content as-is, because it's just so badly done.
Personally, I would be very happy to read an abstract along the lines of 


  ABC is an important problem because of XYZ. A solution to this problem was presented already by UWV et al., but is not widely known, partly because of the technical nature of their presentation. Here we give a readable presentation of UVW et al.'s ideas, showing that they can be interpreted in terms of PQR, and we give applications in the field of JKL.


If the paper is mostly a reinterpretation of existing work it might not get into a top journal, but if the problem is important and the solution is a good one, your paper will be a valuable contribution and is likely to be widely cited anyway, since most people implementing it will be working from your paper and will cite it along with the original.

There is no danger of it being seen as plagiarism if you are presenting their ideas in your own words, and state at the start that this is your goal. The other authors will likely be happy as well, because their work will become more widely known as a result of yours. There is no need to involve them directly at all, although of course this is possible as well.