Other ways to integrate into contact flows
The voicemail solution is rather impressive from a technology standpoint, being completely serverless and offering transcription. Unfortunately, it doesn't provide a lot of permutations for the integration. It's up to you to create the necessary changes to make it a better fit for your implementation.
In the next section, I will demonstrate possible changes that you can make to integrate the solution better. Of course, it's highly dependent on the requirements of your individual call center's needs. This diversity is probably why the solution doesn't include any other options. However, it still would have been nice for them to at least give some ideas.
Removing the extension prompt
The first way you can improve upon the implementation is to remove the need to enter an extension to leave a voicemail. In my opinion, this would be a vital change to make. I have never had to enter an extension to leave a voicemail...