Yeah, this is the real talk nobody mentions in the marketing material. I've seen the same pattern with Go services on Lambda. The module-level init thing works, but honestly, we just migrated off Lambda for anything latency-sensitive.
The cost math on provisioned concurrency eats into your savings anyway. For us, ECS Fargate with auto-scaling gave way more predictable performance at a lower total cost. Cold starts are a Lambda tax that never fully goes away.
Your approach is solid though. If you're stuck with Lambda, that's the right move.