You need to change your IP address (a VPN can help) and use a different browser.
It's really impossible to "permaban" someone if you know what you're doing
1. Reddit analyzes text patterns
They can (and will) identify you based on how you type, correlating it with many other factors. Especially if you interact in the DMs, it's really hard not to get caught, you'd have to be consistently type in a different way during a conversation, it's as hard as changing your speech pattern in every conversation you'll ever have from now on. Theoretically possible, but practically unfeasible.
Maybe you know this, maybe you don't, but many of Ross Ulbricht's accounts, Silk Road's founder (very famous dark web drug marketplace), was caught thanks to this type of analysis, among other things. (they tied many different forums' accounts to a specific account and that specific account to him).
Not only is it real, it's actually rather easy to do in this day and age.
2. Intersectionality
By stacking your interest you get a smaller and smaller pool of users that it could be. Let's take this as an example: user1 likes leather crafting, he works out, plays the trombone, is gay and loves Murakami's books (imagine a much longer list). Now let's say user1 gets permabanned; a couple weeks later, wouldn't you know, user2 shows up and he likes pretty much the same things, and writes in a very similar way. User2
will be banned, too. Not only does this make logical sense, but that's pretty much how I got my permaban, and there's no reason to believe that Reddit was monitoring me more than anybody else.
3. Your email IS tied to you in some way
It's very hard to create an email that isn't tied to you in some way
that Reddit will accept. It wasn't like this before, but now it's pretty much impossible: you'll have to insert your phone number somewhere, or use an email as verification and THAT email is tied to you in some way. I know there are some sites that allow you to create an email without phone number or verification email, but Reddit doesn't accept those.
4. You can't use Tor, really
You could, but based on what I've just said, it wouldn't really change much, they'd still know who you are even if you're pretending to be Finnish. Also, it's very easy to know if you're using Tor or not, and they pay extra attention to Tor users.
TL;DR
True anonymity is almost impossible even theoretically, and on Reddit it's impossible for many reasons, especially if you use it like you were before the permaban. Basically, unless you turn into a completely different person, it's not gonna happen.