To me, the "reciprocal linking being dead" assumption just does not make sens.
If spam-indexing and farm links ever was useful it's another story, but link exchange means many more case than this.
Let's start with defining link exchange :
Link exchange means you are willing to give links to receive some.
Now, the main difference with a strict backlink is that, you'll be as well linking to the domain linking to you.
What could actually cause link exchange to be weak, beside the backlink to be weak in itself (posted on a poor or unrelated page) would be to link back to the page where your backlink is posted, and to repeat this situation for the majority of your backlinks, and even worst, to concentrate all your exchanged links on the same page.
It stating the obvious to say a page with no text content and a majority of external links is poor SEO wise.
But you could a) give a link back from another domain of yours or b) give a link back from the same domain but not linking to the page where you backlink is, and on a page with content and minority of external links.
These two techniques would increase the complexity of the linking strategy and would make it harder for bots to tell these links should be less considered because of some "link exchange moderation" routine.
And actually, I do believe such type of poor link exchange filters exists in SEs, but I'm not sure it's the most important when it comes to take backlinks into account. To me, the quality (content, PageRank and the way it is related) of the page where the link is posted is way more important.
It was often stated that few backlinks could end up weighting a lot more than a lot, depending on their quality.
In this post
, I elaborated a bit on a web site having PR6 with only
44 Google backlinks.
This is how much the quality matters, way more than the link exchange penalty IMHO, if ever was more than just checking if both links would not come from a page with many external links (the typical link exchange page).
I mean, what do you think would occur if you'd get a link back from google.com ? Even if you'd run one or many link back to Google, I'm pretty sure your server would not be able to handle what would follow
The first article you're pointing, supposed to show us link exchange is dead, does in the end not really state more than : "we should fight for the best backlinks".
And the second one does not really enters in contradiction.
What is for sure is paying does not mean much about the link quality, it can be a good thing to pay for a real good link, but paying is not what makes it so good.
Same rules as ever apply to evaluate the possible backlink quality, the fact that it will last in time being one of the most important just after relationship in content and PageRank.
That's probably why, unless you're really rich, paid links cannot be your only backlink source, because they are by definition not supposed to last for ever.
It's all a matter of what are we talking about. I never though running a link exchange page could be of a great interest, but always believed we should exchange links, in a clever way obviously, with well ranked related web sites. And the result depends on the web site we will be able to exchange links with, that's all.
In your case, I suggested you start to try exchanging links with website providing home work services, since it seems to me there must be many small companies (plumbers, tools resellers etc ..) with well ranked and related websites out there, even small.
Because 1) I think there is plenty of such website in the Internet and 2) I'm sure some of them are, despite the fact they are not visited a lot, old thus ranked and possibly very well, with good content, even few.
Do-ability being, as always, what comes first.
A good way to achieve this would be to start an DIY directory with a link back for submission, the goal being to avoid running a page with a majority of external links.
But you can think of many other