HTML problem solved.
Because this plugin does store calendar events in the first post of the linked thread, the calendar event is actually searchable. However, a caveat to this design is that forum permissions override calendar permissions. I had my calendar set to allow html and my linked forum set to HTML not allowed. The forum permissions were overriding the calendar ones. When I set the forum permission to allow HTML, all my calendar events with HTML allowed HTML.
This also explains why moving a post older than the calendar event thread to that thread changes the calendar event. It's why merging threads is turned in event forums. But it is still possible to move individual posts, so your staff must know not to move a post older than an calendar event thread to that thread. There's no protection from moving posts like for merging threads.
I will be working on this conditional in the next two weeks now that the HTML problem is solved.