Survival modeling is exactly what's needed for these situations. It allows you to (a) consider censored data (i.e., active customers who you know stay for at least X months) and, (b) use flexible survival distributions beyond the standard exponential distribution assumed in the typical monthly churn rate calculations.
Source: Run a data science company and we work on a lot of customer lifecycle modeling projects with companies much younger than yours.
Source: Run a data science company and we work on a lot of customer lifecycle modeling projects with companies much younger than yours.