Hi Scott. My name is Uthman Apatira =)
There are tons vendors that provide telephony integration. Twilio is not only affordable, but also feature rich and cross-language compatible. You've made an excellent choice!
Your project notes were much spot on. The only subtlety I'd point out is Twilio wouldn't actually be "reaching" into your DB / email server in order to instantiate a call. Rather our code would direct Twilio, upon a submission, to call the agent and present them the details + conference option using TwiML's Dial command.
WordPress has user CRUD operations built in, and makes use of a MySQL database. Plugins can create additional DB tables on demand, so that's great for us. Besides contact details (Name, Tel, Product, Details, Timestamp, Submission Page, etc.) you probably also want to track the call flow - did the agent pick up? How often they pressed 1? Did the user pick up? Conference duration? Etc.
Twilio offers a lot of functionality, so once you start using the software, we can further expand it. Your imagination is the limit! Anyhow, if you'd like to discuss more, please reach out to me. Looking forward to working with you!
Uthman Apatira