The fact that Let's Encrypt certificates expire quickly is a feature, not anything to do with paid vs. non-paid.

Let's Encrypt could have just as easily generated certificates good for a year or more. But the point of Let's Encrypt is to force you to do this in an automated way, using scripts like you suggest.

You're not getting around anything. The choice was by design.

https://letsencrypt.org/2015/11/09/why-90-days.html