On day 2, at the start of day 2, 2pm, it should be possible to both record Buchelli's phone call and talk to Wilkes. That's what I remember, that's what the walkthroughs I tried to look this up on say, and both actions give you points so it's needed for full score.

However, after I record the phone call I literally have only about 1 second before Buchelli comes out and starts drinking with Wilkes. It's far too little time to leave the phone booth and talk to Wilkes. Most of the time I can't even get out of the phone booth, and those times that I do Buchelli immediately comes out so I still can't talk to Wilkes. I've tried this over a dozen times now and I just can't get it to work right. You can't talk to Wilkes first either, because doing that causes you to miss the phone call.

I tried using a slowdown utility (I need to use one for the binoculars anyway), but that doesn't increase the time and just makes it harder becaues the movement is less smooth.

Is there any way around this?

EDIT: Sorry, forgot to mark this as a question, and I can't make it a question now.

Okay, I managed to do it. The way I ended up doing it was by talking to Wilkes first, then turning around very quickly and entering the phone room before Buchelli comes out. It took a couple of attempts to practice the turning around movement (since due to where the game places the camera after talking to Wilkes you need to move slightly to the side as well to be able to see the curtain), but it worked and I was able to see both conversations this way.

It is then also possible to really quickly get out of the phone room and see Buchelli join Wilkes (though that doesn't get you points).

Thank you very much for this. I had the exact same problem, some sort of timing issue makes Buchelli exit the phone booth in a single second, making exiting and talking to Wilkes impossible. Your way requires some very fast panning and clicking too, but it can definitely be done.

I had this problem too. Here's a tip for others with the same problem.

First, I used Turbo, the slowdown utility. This was necessary for me, but still provided very little time.

I started by talking to Wilkes, then quickly moved and panned the camera. I clicked on the entrance to the phone room and clicked the "open/enter" button. (Without Turbo, clicking on the phone room wouldn't even bring up the interface before Buchelli left!)

However, after clicking the button, I also had to press Escape to skip the animation of Gabriel walking. (Otherwise, Buchelli left the phone room before Gabe got there.)

Inside, I tape recorded the conversation as intended. Then, by turning around and exiting the phone room right away (again, pressing Escape to skip the walking animation), I was able to catch Wilkes's chat with Buchelli.

You also have to listen to the entirety of the conversation between Gabriel and grace at the beginning of the chapter. If you skip that scene, you also skip some time, and then this becomes impossible. At least that's what I've found.
Oh cool! I just realized that SvenGroot is Dilandau3000 on youtube. His Let's Play introduce himself as such. Sven, I love your Let's Plays.

The key to this puzzle is not to use 'Escape' at any point. If you use it to skip any dialogue or walking then the in-game timer accelerates significantly. If you do not use 'Escape' from the beginning of the chapter until all the time-sensitive tasks are complete then you'll easily be able to cover everything without needing to use any software to slow down the game.