Given your dates, and assuming that you have the correct dates for Segorbe, this would be my suggestion. Segorbe's might not be as 'big' as Santa Tecla but it is still a major festival, so if it appeals to you at all I strongly recommend you go for it and start making plans on where you can stay immediately.

Please do check the Cardona festival - I'm not convinced it is the 12th to the 15th. If it really is, then ignore what I said about Sergobe as the 12th to the 15th are absolutely perfect for you.

I also really hope you'll report back, I'd love to hear about your experiences there. You'll be seeing so many wonderful buildings and monuments in Barcelona and Madrid, this is a wonderful chance to absorb a whole other side to Spain.