How to create JMeter test with parallel execution in one thread group with specific throughput?

I've got API usage statistics from production cluster and need to simulate it on test cluster, i.e. execute N requests each with specific rate per minute. I've achieved desired result with following structure (simplified):

- Thread Group #1
  - Auth
  - Loop Controller
    - API Request #1
    - Constant Throughput Timer #1
- Thread Group #2
  - Auth
  - Loop Controller
    - API Request #2
    - Constant Throughput Timer #2
- Thread Group #3
  ...
...

It is not looking good enough cause I'm forced to repeat same Auth and Loop Controller many times for each API Request.

I prefer to have test plan structure like this:

- Thread Group #1
  - Auth
  - Loop Controller
    - Some Kind of Parallel Controller
      - Simple Controller or Something Like This #1
        - API Request #1
        - Constant Throughput Timer #1
      - Simple Controller or Something Like This #2
        - API Request #2
        - Constant Throughput Timer #2
      - Simple Controller or Something Like This #3
        ...

The only one looking good tool to implement such solution was bzm - Parallel Controller, but I could not make it work with structure above. Maybe I'm doing something wrong.

Could anybody help me with this?