I put the stripe charge ID as a new column as "source_id" in the CSV export for purchases. Tell me if that doesn't work for you.
BTW, regarding booking. In "direct to you" payments, you are the point of sale and Stripe is paying you. The analytics on itch.io are there for confirmation and convenience, but we aren't the ones paying you. For you booking you should use the numbers the Stripe (or PayPal) provide to you for handling your books.