See the Zelle "getting started" page at https://www.zellepay.com/get-started - there's no solid set of instructions because there's almost two thousand different implementations of it. Your bank's procedure may be entirely different than mine's; if your bank doesn't support it it's a different procedure alltogether.
As a result, scammers can fairly easily convince someone who's never or infrequently used it that their process (usually with a phished website posing as Zelle) is legit. The "it's a banking technology, but it's also a website and an app, maybe, it depends" thing doesn't help.
I don't know the answer, but seeing as Zelle was developed by a consortium of big banks, it's at least possible they simply don't want to support this use case, because making it harder to have multiple accounts benefits incumbents.
I believe a single Zelle identity can only be linked to a single bank account, and a Zelle identity consists of an email address, phone number or both. Typically it's the "both" option, but I think that in theory you could create multiple identities with multiple email addresses, and link each to a separate bank account
If someone impersonates me or steals my debit card, they can do a bad ATM withdrawal and get cash. That can be reversed, but for some reason once Zelle is in the picture everything is written in stone.
It's rare that a lawsuit against a fraudster or thief goes anywhere, but depending on the amount lost, it can be worth it to obtain a default judgment, which can typically be collected for 10 years. If you can identify the person or entity that took your money, they might eventually have enough assets for you to collect.