The link exchanges you mention are troublesome, as it may look like you're moving or redirecting that content (from both sites, actually), to avoid the effects of either Penguin or of a manual penalty... To be discussed.
Coincidentally, I had originally included in my first post, following my comment about Google's long memory, a paragraph about the kind of things I believe that Google does remember. The paragraph made the opening of the post too long, though, so ironically, I dropped it, but here it is... >>It has been discussed with regard to content from a penalized site that Google may remember that content and apply a penalty to a new domain. This content you're discussing, of course, is not penalized... and Google isn't known for rewarding historical originality, so you may be OK.<<
Now that it turns out that it's either been penalized or hit algorithmically, so yes, it's likely that you've got a very tricky situation. (This may be, btw, why the article you like wasn't ranking on that site. I haven't seen the site, so this is just a possibility).
These links however are only to the home page, NOT to the articles on the domain which I am going to be 301 redirecting to my own site. (I do not plan to make a redirect of the home page, only the articles I'm interested in.) Do you think this is a problem?
Potentially, yes... and I can't think of anything good to say about it. Internally in your site, I'm guessing that the effects of Penguin probably flow like link juice does or like PageRank propagates, dropping off as your nav splits and gets deeper from the landing point of the link. So, they'd be flowing from the home page.
If you split the articles off from the home page, you've still got the question of whether Google remembers that there once was tainted link juice going to the article pages, and whether it's keep score on those algo issues.
Your instincts about dropping your reciprocal links are good, and ditto about waiting... and your thoughts about the home page being split away are logical thoughts. I just don't know whether those article pages are tainted by Google's sense of justice (and I don't know how else to put it). A 301 will redirect a penalty or link based algo violations, so if that link taint from the home page migrated through the site, and cutting off the home page doesn't take care of it, then you've got link juice rot flowing through your site nav, putting a label of sorts on each of the pages. I don't know, though, that this is happening; and I am in fact looking at worst case scenario for the sake of discussion.
Have you checked whether there's a manual penalty, or whether it's Penguin, which is algorithmic (and in some ways perhaps worse because of Google's desire not to make the update dates clear)?
It's late for me here, and I'd planned to get to bed early, because I have a very full next week. I think you understand most of the link problem considerations, and that your instincts are good. The only really safe way, though, IMO, may be to clear up the linking situation completely, disavow if that's necessary, clean up your act, etc.
If it's an algorithmic situation, you may have a long wait. I'm thinking that...
(a) Google wanted to make this algorithm memorable...
(b) Google is taking forever to straighten it out...
(b) straightening it out quickly may be impossible, as you've got layers of bad stuff that need to unwind like entropy (if it 's even theoretically possible that entropy could unwind). In this case, there's been layer upon layer of compounded confusion and crappy links.
I know I'm leave a lot out in the interest of time.
I can't say right now whether I'd go for Option 1 or Option 2, except to say that I would NOT remove the URLs via the Search Console. That's a separate discussion, but I think long term effects of that would be a disaster. Maybe you could use robots noindex meta in the old sites, but ultimately you'd want to drop it. I'd have to think about the alternatives.
The canonical tag has its own idiosyncrasies, btw, that ought to be discussed.
I myself would keep the author's byline on your pages. Not sure whether he should link to the moved pages if you use the canonical. I have a respect for authors, and I think that Google is developing an awareness, and I would be careful of trying to sweep history under the rugs. I think I'd go the other way, and acknowledge his contribution to your site. In addition to all else these days, you've got him as a named entity, with knowledge graph issues coming if not there already. And I do think, if he really is a known authority, that his name, marked up properly, will be valuable as something like topical PageRank and other "socially" related ranking signals roll out, assuming this hasn't done so to some degree already.
The articles sound fine, but I don't know how Google looks at such transactions. I think they'd respect it more if you keep his name, and gave him an author page. Too bad he swapped links and maybe tainted the situation.