We've hit the throttling issue many, many times. Everything about Parameter Store is difficult. And its a shame. Its such a simple concept. They have enormous resources, so why not throw a couple of devs at it?
In any case, we do also use redis. It might be worthwhile to pitch an idea to move over to that. But we pull the parameters in bash scripts using a custom tool called aws-env, so we'd probably have to make or find something similar for redis.
I believe this is a new(ish?) feature, but someone from AWS Support recently pointed it out to me when dealing with throttling issues. Might be of interest to you.
In any case, we do also use redis. It might be worthwhile to pitch an idea to move over to that. But we pull the parameters in bash scripts using a custom tool called aws-env, so we'd probably have to make or find something similar for redis.