No, we only have just the one org, 

See screenshot for the past two hours. We are not even close to 10 requests per second. We made in total 2061 API calls. This is roughly 1 call every 3.5 seconds 

Thanks, we already throttle API calls to 1 call every 10 seconds and still hit the rate limit. Action Batches won't work for our use case as they only support write/update operations, not data retrieval.Our goal is to get a full connected client list...

Yes, rate limiting is only on getNetworkClients. 

The issue Erisan is referring to is the API endpoint for getNetworkClients; This returns a list of all clients. There is no Org-wide endpoint, and you have to do this for each site.