Optimize WooCommerce SiteGround Resource Usage

My WooCommerce store on a shared SiteGround plan keeps hitting their resource ceiling. SiteGround automatically suspends the site several times a day and their logs show waves of unfinished SQL queries piling up until new requests tip us over the limit... (Budget: $10 - $30 USD, Jobs: cPanel, Linux, MySQL, Performance Tuning, PHP, Web Hosting, Website Optimization, WordPress)