Are there any special considerations for taking experiences that I have created on one PC using my original Composer license, and they copying those experiences to a new PC using a new composer license under a different account? Or does in not matter?
Since the previous license does not match the current license you might have issue opening the experience in Composer. If that is the case then you will want to open a ticket with support and they can assist you.
Here is a link to open a ticket with support.