Well then, that sure was a weird root cause!
After spending some time with tcpdump I noticed my Discourse host reaching out to text-lb.esams.wikimedia.org on port 443 right after I click the bookmark icon. Our firewall drops traffic it doesn’t like instead of rejecting it, and that often causes sessions to hang for a while.
The problem was that I had “enable inline onebox on all domains” turned on and since the next message in the script from discobot contains three wikipedia links it got hung up on something in the onebox handler for too long. As soon as I disabled that setting everything works fine and discobot responds right away 
Sorry about the unsupported edge case, this installation is using the How to install Discourse on an isolated CentOS 7 server method which makes my life harder than it has to be (at least until I can convince the security guys at work that Discourse isn’t scary and just let it have internet access)