I've worked remotely my entire career and one shared aspect of the most successful teams was a chat room named "watercooler" or similar where people were free to chit chat. Everyone knows to ignore the room if busy, so there's not that worry of IMing someone and distracting them. Some times people may reply back hours after you say something, but when a few people have spare cycles at the same time nice conversations can break out.
It's curious to me how when a lot of discussions on remote workers, especially those negative to the idea, I rarely see mention of chat rooms, when I've used them at every single place I've worked remotely. Most of my career success is due to connections I've made on IRC. I don't think this is that rare of a scenario, see the #w00w00 folks.
In the era of "catfishing" where people can fall in love with people based solely on chat and online relationships, I think it's hard to deny it's possible to form meaningful connections online. Emails, conference calls, and video conferences aren't going to do it. If you spend 8+ hours a day "talking" to some one in a chat room, you can learn more than 15 minutes at a water cooler now and then. As well, the whole team/group can read the backlog and know what's going on with everyone else. No need to repeat the same story to x, y, and z.
I agree with what you've said about having some informal conversation during lulls on calls. Those moments can be very valuable. Another thing I've done on some teams is after a major release or milestone achieved, everyone grabs a drink of their choice and joins a group video chat and virtually goes out to the bar to celebrate as a group.
Lastly, one of the things I've done is occasionally send small gifts to other team members. As an example after explaining rubber duck debugging to a team member who solved their own problem immediately after asking me and wasn't familiar with the term, I sent them an awesome rubber duck overnight. (Total cost <$10 via prime)