Integration between ElevenLabs Agent and HeyGen to Reduce Latency

Hi,
We're currently integrating ElevenLabs with HeyGen. Our setup allows the ElevenLabs agent to handle full conversations with users, and we use HeyGen’s interactive avatar to deliver the responses back to the user.
Here's our current flow:

The user speaks to the ElevenLabs agent.
The agent responds with text.
We call the /v1/streaming.task API from HeyGen to trigger the avatar to speak.

In summary:
User speaks → ElevenLabs Agent responds → Response sent to HeyGen API → Avatar speaks

The integration works well, but we're noticing some latency — there's a noticeable delay between the agent's response and when the avatar begins speaking.
We're exploring whether it's possible to connect or integrate the ElevenLabs agent directly with HeyGen through an MCP tool, so the agent's responses could be streamed directly to HeyGen without manually invoking the API. This might help reduce latency and improve the overall responsiveness of the experience.

Could you please confirm if such an integration is currently supported, or if there's a recommended approach to achieve this?