How about
1. Get the call queue members once every morning and store them in a local cache/ database. Use the data from this cache throughout the day to get the details you want.
2. Depending on your use case, you can run this process of syncing the members more than once a day
3. You might have to implement a batch process at your end to make limited calls per minute so that the rate limit is not exceeded
P.S - The catch is that if a new member is added to the queue, you might not be notified since I did not find any notification event that delivers such information
Could you share more details on what do you do with the queue member data and your use-case around that?