How would I go about creating a customization to search for orders/customers by a product in their order
You can use the Moco Insight extension to do this. Easy to install with a 14 day trial so you can play around with it to see if it suits.
Hello @aesquenazi
You may check this Order Management Magento tool. It lets you add a column with products names to the Orders Grid, and then sort orders by a product.
Also you may use these 2 free extensions:
http://www.mageworx.com/products-ordered-by-customer-magento-extension.html
http://www.mageworx.com/product-orders-by-customers-magento-extension.html
Hello @aesquenazi
You can also check out this extension https://amasty.com/better-order-management.html
It will provide you with wide functionality for orders proccessing.