Nevermind – I found the solution. I had to add this code to my htaccess file, which I thought I had already done, but apparently not:
<IfModule security2_module>
SecRuleRemoveById 114
</IfModule>
Tried connecting again to the Publicize feature and it worked just fine. What suprises me is that in the past I haven’t been able to connect to Jetpack at all without that code being added, but I was able to do so this time at least partially.