What's the cheapest and secure way to make alt accounts that require phone number verification?

I haven’t tested it myself, but you could try generating a 10minute email [https://www.minuteinbox.com/] and signing up with it. Some websites allow it while others don't. Let me know if it helps 💪🏻

Use a sms service like smspool

One could use MailDrop to sign up.

Downside is that you could go back to the site and check their email again making it a potential security risk, that is unless the account isn't worth pennies!