What about an app that only records one side of the conversation (your own voice). This recording could be triggered whenever you hold down the side (volume, camera, etc) button on the phone. So, as you're talking about thing and you repeat important notes back to your client you can simply hold down the side button while you're talking and those will be recorded into a voice memo when you're done. Let go of the side button when you're done saying the part that needs to be recorded.
Once the conversation is finished, the app could automatically generate a text-based writeup of the notes you made along with a timestamp for when you said them.
Sounds good to me. I could certainly use this app.