Hi @Rob S.
I hope this info is helpful to making sense of the best way to calculate things in your company.
Churn is calculated when a paying customer no longer pays. If your customers are signing up without paying anything and they leave, they are not a churned customer. They're a user who hasn't converted into a paying customer.
A metric like 'no logins within X period' might be helpful to determine activity and then create a sequence to help them re-activate.
You might also want to talk to some of these customers to find out why they don't stick around. Even interviewing 10 of them could help identify other possible routes to monetization besides the route you currently have.