Creating emails and reattempting the sign up process with these will indeed allow the scammers to create accounts but it will significantly slow down the ones that are using this route. We need to plug the simple holes.
Limiting them per IP address would be a good idea as well. It would give them another hoop to jump through. Let's say 2 accounts per IP.
Like you said, there's another solution that would add another layer: have the SMS receive a number and then SEND it. That will eliminate the receive-only SMSes.