You should definitely also include your updated resume, prominently calling attention to any new and upcoming engagements, in these letters. It goes the extra mile to complete the self-promotion package and show that you are busy and always taking on new projects. You don't need to go on and on about your resume - that's tacky and insincere when couched in a thank-you note like this. In fact, you might not mention it at all in the note, but just enclose it in the envelope.
But second, there's something in your post that seems a little odd to me. Are companies mailing payment after the show closes? In every professional show I've ever done, I walk out the door after load-out with a check in my hand. When someone says "I'll mail it to you" I say "No, I'll take it now, thanks." Because otherwise, I never get a check. It is entirely standard to receive your full payment immediately upon closing the show. I do understand that sometimes smaller theatres say they'll mail checks; they've tried to say it to me. But it's always, always in my contract that I am paid in full when I walk out the door for the last time. I don't mean to be a Cassandra, but I would really encourage you to take up this practice, because if you haven't been burned yet, you will be one day.