I totally agree with you regarding Child Theme support. I’m a bit disappointed as well when it comes to WP themes code.
did you create the app from your twitter account? You need to place some keys in the index.php file.
I didn’t modify anything else in that php file so you can leave the private $lib to the default one.
Also, use the absolute path to the index.php file. Please check this answer: https://github.com/seaofclouds/tweet/issues/264#issuecomment-20092593 – you’ll end-up with something like /wp-content/themes/themename/js/twitter/index.php (put the correct path to your script)
Good luck with that.
Please send me a message using the form on my profile if still interested.
Maybe static variables will help you.
Looking at fiverr… and thinking that we might work for peanuts pretty soon.