I just wanted to check to be sure you received my previous message. I have looked at your daily appointment project and I know it can be done. If you want to discuss it, contact me at my personal email address: firstname.lastname@example.org
Sorry, I have been busy with some development projects and Christmas and did not check the forms at all yesterday or today until just a few minutes ago, so I did not see your message.
I have not tried to do exactly what you are wanting to do, but it would think that it could be done. You state that you want to " display the day in 15 minute intervals", but I am wondering how many hours of the day you want to have available. Do you want all 24 hours?
I assume you would have some form where the appointment would be created and then that appointment would then be displayed in the daily log view.
I can think about it and see what might could be done.