What a wonderful story and quilt! You did a great job with the quilt and quilting. The sharpie markers are soluble in alcohol, so the hand sanitizer option may work due to the amount of alcohol in it. It might be helpful to try using just a bit of rubbing alcohol on its own to see it that will work as some hand sanitizers may have lotions, etc. in them that would add other types of stains to your quilt.
Rob