Incoming Calls with higher priority than Callbacks

Hello,

We recently launched Zendesk in UK for our support operations and we identified a possible problem with our team. The team is constantly receiving callbacks and not having time for incoming calls.

Our IVR is structured in a way that it does not have a callback greeting as it is one single message with the callback instructions after 3 min of wait time. This makes it impossible to avoid callbacks being shown to the agents if there is also another incoming call, leaving them constantly accepting callbacks.

Is there anyway to filter the callbacks? We thought about doing it via queue but we can't filter the callback before reaching the agent (only after with accepted or rejected). How can we make sure that callbacks are not a priority?