Okay, I missed the whole "Create both holidays when your founder dies" part. Sorry about that.
Also, I found that I was panicking for nothing - the calendar refreshes the season you are on after you enter the next season, so once it becomes Summer, it'll pull Summer up to the top and bring Spring back. (I did this by doing a test file and using a Seasons cheat to advance the season.) Thankfully you saved me from invalidating my legacy by pointing out that rule about when I have to create my holidays. I knew that one holiday was the deathday(Harry Potter reference) of the founder, but I didn't read carefully. Sorry about that.
If anyone wants to close this topic, that's fine.