So don't let people use your services without paying! A trial is only a trial if it locks or stops the user from using it after a trial period. Freemium models that limits number of uses aren't a trial.
Ultimately, my solution was to start requiring a credit card at sign-up. Shockingly, not a single mailinator.com address was used from that point forward and my conversion rate barely changed. But, it sucks I had to do that. There were people that legitimately wanted to try the service out that were put off by requiring a credit card so early. I personally hate providing a credit card for a service I haven't even tried yet.
I appreciate your reply, but I think it's an entirely toxic mentality. My business model isn't freemium because you could game the trial process (and violate the terms of service). And I shouldn't have to grossly restrict the trial to deal with mailinator.com sign-ups. Say what you will about mailinator.com, but it was hands-down the largest source of abuse of my CI-like service. Everyone else played by the rules and enjoyed a liberal trial to get familiar with product.
This is great! You have users who are using your product, how could you not be happy? Find out why they are not converting, perhaps your offer isn't that great for their demographic? Note that even if they didn't pay to your service, they may be your biggest fans who may recommend your product to other people. DEA users are usually tech-savvy types, they are also the kind of people who are the early adopters when it comes to tech (since they were able to figure out how a DEA works & how to use one), and are probably the ones who normal people go to get advice. Don't forget that even if not a paying customer, they are still a customer in the sense that they could review your service or refer others through word of mouth! If you're blocking DEA services, it may end up costing you more.