Hey Laura,
Thanks for reaching out to us!
The iCal Importer sounds like it could work for this site IF there is a global .ics feed that is generated for all the events on the site. If so, that would be the simplest approach.
If not, the best approach would be to grab the events from the database as a CSV and then ensure the fields match up to the basic importer found with our plugin and import a CSV that way.
I’m sorry I wasn’t able to give you a direct answer here but hopefully it helps to get you pointed in the right direction.
Thanks!