Imagine the next scenario: a user wants to register to a webpage and fills a form. While he is filling the form, jQuery keeps checking through a regular expression if fields
This type of attack can be treated the same as any other brute force attack, where the only effective solution is to use a Captcha. But of course, Captchas are a detriment to UX, so you have to consider if the additional security is worth it, especially for an attack that is very unlikely to happen anyway. That said, you may want to use a Captcha on your registration form anyway, to prevent bots from creating accounts.
This sort of attack has a huge cost for little reward for the attacker. There are billions of possible email addresses to test for. It could only be worth going to great lengths such as this, if the site in question was particularly sensitive, such as some kind of adult site, where the attacker hopes to blackmail users that he finds.
CloudFlare
Not as good as a Captcha solution but the brute force attack might be detected and prevented by CloudFlare's DDoS system. Also, CF can force Tor users to solve a Captcha before accessing your site, which would prevent an attacker from using Tor as a vehicle for the attack.
IP Rate Limiting
Rate limiting on an IP basis has problems because if an attacker decided to undertake a task as huge as this, he will likely be using a Botnet or some other system of multiple machines to launch the attack.
Consider a large organisation such as a University, where all users share the public IP. One of the users launches an attack on your site, and you block his IP, and in the processes blocking everyone else. This countermeasure could actually be used to launch a DoS attack.
Session ID/CRSF Token
Definitely not a solution because the attacker needs to simply make a request to the page first, to obtain the token. It's an additional request to make but only an inconvenience for the attacker.