It would require first that you insist people give you more details when requesting to join than just an email. And gather more detils like IP address. Get real name, address, phone #.
Second it would require a team of people working to vet everyone trying to sign up to see if they are real people. You can do some very basic things like:
Google the persons email address and see if they have a history of it being used, and what kind of websites.
Check and see if the name, phone number and address given match up with any public records.
Look at the address given and the IP address used to sign up- someone claiming to be from rural GA with a San Francisco IP should demand questions be answered first.
Most states allow the public to search voter registration records, so an obvious one would be to check those. If someone attempts to register and says they are a 35 year old named Shane Grimes from Georgia and you cant find any registered Democrats or Independents in GA by that name it should be a red flag.
And lastly, actually make a phone call before activating a new registration. A few words on the phone can usually give an answer. If Sarah Wilson from Arkansas answers with a male voice and a Russian accent that is a giveaway. You can hide accents a lot easier online than over the phone.
Also, ban the IPs of known proxy servers so people cant hide their IPs.
All that wont stop them all. But it will make it much harder for them and since they seem to like volume would probably cause them to go elsewhere.