I have made a temporary fix by disabling the Javascript that loads content in place. As the correct url is there in the HREF, disabling the JS just allows the next and previous buttons to work as regular links.
I couldn’t be bothered going through all the JS and manually editing; I want a fix ASAP. So all I did was rename the files:
tribe-events-ajax-calendar.js AND
tribe-events-ajax-calendar.min.js
to
xtribe-events-ajax-calendar.js AND
xtribe-events-ajax-calendar.min.js
Voila, links work fine again. No adverse side effects that I’ve seen, other than links load normally.