I'm so glad you guys are prioritizing this! Note that the comment ahead is focused on DMs. But I acknowledge incentiving DMs isn't the only (or even best) way to encourage useful connections. Here goes:

Yes, I DMed an author of a post, he responded favorably, and we met at an approaching EAG to talk further. This was useful and we agreed to remain in each other's networks, eg hear about successes to implement in our similar work, or be on hand for advice as needed.

Special context: He had posted a piece on a topic I had experience on. I agreed with his premise but not the weighting of the variables, which led him to sort of dismiss to the reader one variable I thought was key. He had written a request for feedback at the bottom so it was clearly okay to DM. I considered writing my message to him as a comment on the post but was nervous to stick my neck out on that particular issue in public, which in retrospect led me to make my dialogue even more open given that it was private, and which led to a more intimate connection.

What improvements this might suggest:

1. For the Author: There is something in here about increasing norms to request feedback, maybe a prompt button/form when you submit the post: 
   
   "We at the EA forum are trying to incentivize deeper connection: Are you (or a collaborator or assistant) open to receiving DMs or email in response to your post?
   -Yes
   -Yes but only of this type: [input private feedback you are really seeking]
   -Yes but not of this type: [input private types of feedback you are worried you'd get swamped by]
   -Yes but I strongly prefer feedback to be public comments for the good of discourse. However, private feedback is better than no feedback.
   If you select yes, there will be an obvious tag at the top and bottom of your post indicating your preference. We still strongly recommend putting a section at the end of your post. These posts [embed a couple timeless posts with good example] provide a good blueprint."
   
   If going with the button option, a drop-down selectable list for types of feedback could also be good (eg, collaboration/job requests, private critique, social reasons, advice, request for advice from you, [blank]). Wow, just realized, imagine if you could put you are looking for "social requests" or something, and that was searchable along with topic tag. Good start to an intellectual social network! Okay moving on:
2. For the Reader: There is also something here about increasing norms to DM things if unsure or intimidated. When I started writing, I started writing as a comment then realized I didn't want to post it publicly. So I copypasted to a DM. I wonder if having "DMing is an option too" within that grey text in the initial empty comment box would be good? Have to word it so it doesn't disincentivize public discourse.
3. UI could be more clear: Also, when I went to DM, I found it kinda hard to find the button on their profile. In at least one time past I assumed DMing wasn't an option (and told my friend I was surprised you couldn't DM on the forum, oops). Maybe it truly wasn't an option back then, but I suspect whatever button back then didnt stand out to me. The current blue button (maybe different maybe not) to message also doesn't stand out to me (though I found it, yay, and that your inbox is pretty obvious in your dropdown user menu clarifies that, yes, DMs are  real thing, keep looking). On the user's page, I really expected the DM  button to be an icon in sequence with all the other icons under their username. But instead it is its own button far to the right of the screen.
4. Clarify norms: It was also unclear it me how much DMing is in norms or not. And I was pretty shy about it and didn't reinvestigate the ability to DM for some time, because I wasn't sure it would apply to me anyway. Eg, do people check their DMs? Is it socially seen as inappropriate and too intimate if you have no connections with the person, and if there is no email dropped at the end of the post, that is a signal that they don't want to be reached at all? Some clarity on cultural norms would be good, somehow! (Though maybe this is redundant and points 1 2 and 3 would be the mechanisms to doing that)

Hope that helps. I tend to go on but hopefully a detailed user report and ideation is useful for impact. This is a high priority project! Again, I'm so glad you guys are prioritizing this!

My initial answer was yes. But now that I think about it, all my EA connections have happened off-forum. Mostly on slack, email, and Facebook. Which I feel is kinda weird 🤔