Hi Nick,
Thanks for your interest in Events Calendar PRO! At this time, it is not possible to make a random recurrence series like you’re looking for. The best option for you would be to duplicate the events with a post-duplicating plugin and then change the dates to suit your needs. Would that work for you?
We are working on making our Recurring Events feature more robust and flexible for situations like this. I’d love to have you add your votes to our UserVoice thread. You can also subscribe to that thread, which will be updated as we progress. Let me know if there’s anything else I can do for you.
Best,
Leah