What is the best way to prevent unexpectedly high charges for a specific AWS service?

I'd like to know what's the best way to avoid unexpectedly high charges for a specific AWS service.

Setup

• Using AWS Polly text to speech service
• A specific IAM user with a specific policy, only allowing full (*) access to the particular service
• A budget action that assigns a read only policy to that user when a certain threshold of the monthly limit (in terms of costs) is reached

Possible problem

This setup works, but the problem is that once the threshold is reached, the execution of the budget action (here: assignment of the read only policy) takes quite a long time - I've tested it and it took about 20 hours(!) before the restricted policy was assigned.

I've also looked into AWS Quotas, but they don't seem to be the right solution as they are a very generic way to control the amount of request. Additionally, they can't be reduced but only increased.

Other solutions or steps to take?

Is there any AWS related way to further prevent being charged large amounts of money when someone (be it deliberately or accidentally) abuses the service? In the worst case I'll have to cover costs for about a whole day (see above) before any restrictive automatic measurements will be taken.

I can run the code from my backend and also implement some type of rate limiting, but still...