If you have only a few contacts who will be reaching you, you might use email to keep in contact.
You might accept incoming texts for free, and respond in a different manner.
Can you borrow a phone from a friend for the trip?
Roaming charges for Cuba are as follows:
Text: 60 cents/text outgoing, free incoming.
@OP: looks like your phone uses standard sim card size (which is a good thing, because I don't think they'll let you cut a rental sim card). A few bucks on eBay will get you the unlock code, assuming your phone is still carrier-locked. My understanding is that you can rent a Cubacel sim card from the hotel, and top up using various online services.