If you don't want to charge per request, you could also offer two pools of backend servers: free servers that are provided on a best-effort basis with fair-use-policy, and paid servers that are exclusive to people in the $150/month plan.
The latter should be easier to manage with more predictable traffic, while giving you more leeway to deal with abuse on the free servers if it ever becomes an issue.
Yes, I was thinking about that, it might actually be a good idea. Provide a premium service with SLAs, while providing the SLA-less service for free, with two pool of servers.
As a user, free or paid, it'd give me a lot more faith in this living past tomorrow.