Hi @MattF
Molly here from AvisPlus Product Options - Customize Product Options & Increase Conversion Rate. Just looked at your requirements and I think our FREE app is a good fit. Our app can let you list out different price options with different flavors and gift box options using conditional logic features. You can also offer more than 3 product options.
I made a demo for you on our official demo store. Please check and let me know if you have any other questions (we also have live chat in our demo store): https://avisplus-demo.myshopify.com/products/pizza.