@max welcome to the Forum! Right now folks can use Custom Availability to control the start times they need each day. (Setting specific Start times) The challenge with offering 40 minutes is that everything is built around the grid display increment you have set. So by default with a 40 minute duration and increment you can only have start times every 40 minutes. If this is adjusted to 10 minutes that will allow start times at the top and half hour. Coupled with the Custom Availability times this will allow for more start times while having a 40 minute duration.
Our product team has been looking at scoping out a solution that will allow users to select a specific start time or internal (top and half hour) and a duration so make them separate. What other requirements do does your team need?